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

Nil

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

Groton (New London County)
First Baptist Church At Old Mystic
Baptisms
The following entries are from the IGI and Vital Records North America (LDS):
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)

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)
1707 Oct 27 Hannah & Samuel, the children of 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
Marriages
1734 May 31 Cyprian Sterry & Elizebeth Ross (Source:Early Connecticut Marriages: Fourth Book: page 34: Ancestry.com)

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)