Hatch:Falmouth Births and bp = BAPTISMS Elizabeth, d. Samuel, bp. Sept. 13, 1772. CR1 Abitha, s. Samuel, bp. Sept. 13, 1772. CR1 and also Rachel, d. Samuel, bp. Sept. 13, 1771. CR1 Martha, d. Samuel and Martha, bp. Oct. 1, 1780. CR1 Rhoda, d. Samuel, bp. Sept. 13, 1772. CR1
Maybe you could locate either the records of a sister of this Elizabeth to compare.All these related records appear to be from "CR1" = First Congregational Church
This Samuel below - is in the correct timeframe, however he died in Falmouth, not ME, don't know that he would have moved to ME with dau and son-in-law.
Samuel, s. Edward and Abiah, Aug. 16, 1738. Samuel, s. Edward and Abia, bp. Aug. 27, 1738. CR1
Deaths in Falmouth Samuel, s. Edward and Abia, Oct. 1, 1803, a. 63 y.
Marriages: Possibility??? of parents Samuel (Lemuel. CR1) and Martha Chadwick, Nov. 2, 1760.*
Chadwick: Martha, d. Samuel and Elizabeth, Sept. 8, 1740. Martha, d. Samuel and Elizabeth, bp. July 4, 1756. CR1