The Congregational Church was predominant in early Connecticut and was the state church until 1818. Other prominent churches in the state are the Methodist and Episcopal [Anglican] churches (pre 1776), and the Roman Catholic and Baptist churches (19th century).

Information on IGI coverage for Connecticut was taken from the website by Hugh Wallis: IGI Batch Numbers for Connecticut

NAVR = North America Vital Records

The following church records have been searched without finding any STERRYS or similar:

Ansonia, Windham County, New Haven County, First Congregational Church (Baptisms 1850-1961-Church Records-LDS Film 1007920)
Ashford, Congregational (Baptisms 1718-1812-Church Records-LDS Film 1007920; Marriages 1719-1812-Church Records-LDS Film 1007920; Deaths 1791-1834-Church Records-LDS Film 1007920)-Church Records-LDS Film 1007920;
Bozrah, New London County, Congregational (Baptisms 1739-1843-Church Records-LDS Film 3727; Marriages 1740-1843-Church Records-LDS Film 3727; Deaths 1737-1751, 1815-1843-Church Records-LDS Film 3727)
Colchester, New London County, Calvary Protestant Episcopal (Baptisms 1864-1885-IGI; Marriages 1864-1895-IGI)
Colchester, New London County, First Congregational (Baptisms 1732-1875-NAVR; Marriages 1732-1783-NAVR)
Farmington, Hartford County, Episcopal Christ Church at Unionville (Baptisms 1845-1883-IGI; Marriages 1845-1885-IGI)
Griswold, New London, Second Congregational Church at Jewett (Baptisms 1825-1861-IGI; Marriages 1832-1857-NAVR)
Lebanon, New London County, First Congregational Church (Marriages 1712-1775-Connecticut Genealogy Trails)
Lebanon, District of Goshen, New London County, Second Congregational Church (Marriages 1730-1799-Connecticut Genealogy Trails)
Lisbon, New London County, Newent Congregational Church (Baptisms 1724-1885-NAVR; Marriages 1724-1895-NAVR)
New London (New London County) First Congregational Church (Marriages 1697-1800-fhlfavourites-Connecticut)
New London, New London County, First Church Of Christ (Baptisms 1860-1875-IGI)

The following church records have been searched and have located STERRYS or similar:

Groton (New London County)
First Baptist Church At Old Mystic
Baptisms 1754-1899 (IGI and LDS Vital Records North America)
1831 Aug 6 Parthenia Sterry d. _____ (Extracted from Church records, 1754-1899  First Baptist Church at Old Mystic)
1843 Feb 9 William Sterry d. _____
1874 May 24 Celie E Sterry d. _____ (Extracted from Church records, 1754-1899  First Baptist Church at Old Mystic)

Norwich (New London County)
First Congregational Church
Baptisms 1700-1886, 1892-1916 [LDS Film 5069]
%%1836 May 7 Francis Asher Sterry
%%1842 Jul 3 Edward Augustus Sterry
%%1842 Jul 3 Catharine Amelia Sterry
%%1842 Dec 25 John Augustus Sterry
%%1842 Dec 25 Annette Rebecca Sterry
%%1842 Dec 25 George Edward Sterry
%%1842 Dec 25 Frank William Sterry
%%1845 Oct 25 Edward Augustus son of E.A. Sterry
%%1848 May 28 Tulley Whittlesea of Ed A Sterry
%%1848 May 28 Catharine Amelia of Ed A Sterry [twin of Carolyn]
%%1848 May 28 Carolyn Augusta of Ed A Sterry [twin of Catharine]
%%1901 Sep 8 [born 3 Jun 1894] Frederick Albert Sterry [of] Charles C & Agusta (sic) L
%%1901 Sep 8 [born 21 Mar 1896] Robert Wellis (sic) Sterry [of] Charles C & Agusta L (sic)
%%1901 Sep 8 [born 19 Mar 1897] Howard Sterry [of] Charles C & Agusta L (sic)
%%1901 Oct 6 [born 29 Jul 1900] Edward Logan Sterry [of] Jabez & Bertha
%%1902 Jun 8 [born 22 Sep 1901] Harold Lee Sterry [of] Frank C (sic) & Louise A
%%1903 Jun 14 [born 1902 Aug 12] Charles Theodore Sterry [of] Charles & Agusta (sic) W (sic)
%%1905 Jun 11 [born 12 Dec 1904] Florence Allen Sterry [of] Frank C (sic) & Louise A Sterry

Norwich (New London County)
First Congregational Church
Marriages 1829-1834, 1893-1916 [LDS Film 5069]
%%1859 May 3 Ralph H Park of Norwich Conn to Anna R Sterry of Norwich
%%1860 Jun 7 Charles Sterry of Norwich to Anna Logan of Norwich
%%1872 Apr 10 Charles Sterry & Winifred Hughes both of Norwich
%%1872 Sep 24 Albert P Sterry of Norwich & Ida M Brown of Lebanon
%%1900 Dec 6 Frank Edward Sterry [age] 25 [Residence] Norwich Town & Louisa Allen Lee [age] 33 [Residence] Norwich Town [where] Norwich Town [by] Rev C A Northrop

The following additional records are included in the records of the First Congregational Church of Norwich:
Members admitted to the church:
1842 Jul 3 Edward A Sterry [Baptised]
1842 Jul 3 Catharine A Sterry [Baptised]
1849 Jul 1 Geo E Sterry
1849 Winifred Sterry, [how received] Conf(ession of faith), [date of removal] 7 May 1908
1871 Dec 31 Dismiss to the South Presh church in Brooklyn N.Y. John A Sterry and his wife Climena
1882 Jan 1 Ida M Sterry, [how received] Conf(ession of faith), Bapt, [date of removal] 10 Dec 1916
1885 Mar 1 Mrs Louise A (Lee) Sterry, [how received] Conf(ession of faith), Bapt, [date of removal] See Vol VI
1886 Jul 4 Bertha (Wagner) Sterry, [how received] Conf(ession of faith), [date of removal] See Vol VI
1891 Sep 13 Agusta (Wagner) Sterry, [how received] L(etter from Church granting membership) Central M.E. Ch (this) City
Church Members:
1837 P, Francis A Sterry
1842 P, Edward A Sterry, d 1874
1842 P, Mrs E A Sterry/Catharine A w. E.A. Sterry, d 1874
1848 Jul 1 P, Annette R Sterry, d
1849 P, Annette R Sterry m Ralph H Park, d
1849 Jul 1, P, John A Sterry, d
1849 Jul 1, P, Geo E Sterry, d
1864 Jul 2 & 1865, Ld, John A Sterry, d
1867 Jan 6 P, Carrie A Sterry
1867 Mar 3 L.d., Climena w John A Sterry, d
1885 b, Marvin W Sterry
Members Removed:
1908 May 7 Winifred Sterry, [how removed] d[ied]
1915 Dec 10 Ida M Sterry, [how removed] d[ied]
Delegates:
1916 May 4 Marvin W Sterry, New London Assn of Congl Churches and Ministers

Preston (New London County)
First Congregational Church
Baptisms (Source: Bi-Centennial Celebration, First Congregational Church of Preston, Connecticut, 1698-1898, Statistics of the Church Taken From The Church Records); 1721-1855 (IGI)
%%1707 Oct 27 Hannah & Samuel, the children of Samuel STERRY
%%1708 JUn 6 Cyprian, son of Sam'l STERRY
%%1711 Jul 22 Robert, son of Sam'l STERRY
%%1713 Jun 28 Zerviah, daughter of Samuel STERRY
%%1756 Jun 27 Mary, daughter of Roger STERRY
%%1757 Mar 3 Arthur, the child of Roger STERRY
%%1759 Mar 11 Mehitabel, daughter of Roger STERRY
%%1761 Oct 11 Consider, the child of Roger STERRY
%%1764 Oct 21 Roger, the child of Capt. Roger STERRY
%%1766 Nov 2 John, the child of Capt. Roger STERRY
%%1769 Apr 2 Abigail, daughter of Capt. Roger STERRY

Preston (New London County)
First Congregational Church
Marriages
%%1763 Dec 8 Silas Sterry & Olive Killam (Source:Early Connecticut Marriages: Seventh Book: page 42: Ancestry.com. Also Bi-Centennial Celebration, First Congregational Church of Preston, Connecticut, 1698-1898)
%%1773 Jun 23 Daniel Kimbal & Mary Sterry (Source:Early Connecticut Marriages: Seventh Book: page 43: Ancestry.com. Also Bi-Centennial Celebration, First Congregational Church of Preston, Connecticut, 1698-1898)
%%1792 Oct 4 John Sterry & Rebecca Brumley (Source:Early Connecticut Marriages: Seventh Book: page 45: Ancestry.com. Also Bi-Centennial Celebration, First Congregational Church of Preston, Connecticut, 1698-1898)
%%1794 Apr 1 Israel Park of Stonington & Abigail Sterry of Preston (Source:Early Connecticut Marriages: Seventh Book: page 46: Ancestry.com. Also Bi-Centennial Celebration, First Congregational Church of Preston, Connecticut, 1698-1898)
%%1794 Oct 26 Roger Sterry & Lavinia Yarrington (Source:Early Connecticut Marriages: Seventh Book: page 46: Ancestry.com. Also Bi-Centennial Celebration, First Congregational Church of Preston, Connecticut, 1698-1898.)
1796 Jan 3 Sam'l Fagins & Nabby Sterry (people of colour) (Source:Early Connecticut Marriages: Seventh Book: page 46: Ancestry.com. Also Also Bi-Centennial Celebration, First Congregational Church of Preston, Connecticut, 1698-1898.)

Note: There is an Admission & Renewals of Covenant for the First Congregational Church of Preston extracted from the Bi-Centennial Celebration, First Congregational Church of Preston, Connecticut, 1698-1898, Statistics of the Church Taken From The Church Records as follows:
Admissions
%%1758 Jul 16 Abigail, wife of Roger Sterry
Names of those who owned their covenants:
%%1756 Jun 27 Abigail Sterry

Preston (New London County)
First Congregational Church
Deaths

There is the following death extracted from Bi-Centennial Celebration, First Congregational Church of Preston, Connecticut, 1698-1898, Statistics of the Church Taken From The Church Records
%%1794 Jul 11 Wife of Consider STERRY, Consumption
%%1812 ___ Wife of Roger STERRY, Rheumatism

Preston (New London County)
Second (Congregational) Church [later First Congregational Church of Griswold]
Baptisms 1721-1855 [LDS Film 1008714]
%%1734 Aug 11 Roger of Mehetebel Sterry

Preston (New London County)
Second (Congregational) Church [later First Congregational Church of Griswold]
Marriages 1720-1857 [LDS Film 1008714]
%%1734 May 31 Cyprian Sterry & Elizabeth Rose, both of Preston (Early Connecticut Marriages: Fourth Book: page 34: Ancestry.com has 'Elizebeth Ross')

Preston (New London County)
Second (Congregational) Church [later First Congregational Church of Griswold]
Deaths 1762-1855 [LDS Film 1008714]
Nil

Mehetabel Sterry was admitted to the Second Congregational Church of Preston on 3 Aug 1734 and paid 3 shillings to the church account in 1735/36. [LDS Film 1008714]

Stonington (New London County)
Second (Congregational) Church
Marriages
%%1748 May 4 Rogger Sterry & Abigail Holmes (Source:Early Connecticut Marriages: First Book: page 56: Ancestry.com)

[Note: According to Walter Smith in 'The Sterry Family', Samuel Sterry was baptised, as an adult, at the First Church of Stonington on 24 Jul 1692]

%% = Stonington, Connecticut, USA line