Interestingly enough this Susannah Palmer born March 1752 has the same parents - David Palmer and Hannah Lawrence although the locations differ.That is often the case with very early records as the borders between MA/NY/CT/VT/NH changed often.
It may be worth looking into David Palmer of CT. Good Luck
Susannah Palmer Birth: 11 MAR 1752 Norwich, New London, Connecticut VS Birth: 1752Of, Warwick, Franklin, Massachusetts
Both list: Father: David Palmer Mother: Hannah Lawrence Palmer
David PALMER Spouse: HANNAH LAWRENCE Marriage:28 FEB 1740Newent Congregational Church, Lisbon, New London, Connecticut