As far as I've been able to find, Martha "Patty" did not have a twin sister. Page 178 of Brookfield's vital records for Rufus's children has:
Abigail born 1770; Ayres (from previous marriage) 1761; Edwin 1774; Elizabeth 1765; Franklin 1774; Kata (Catharine) 1780; Patty 1778; Persis 1767; and Susanna 1768. William is not mentioned here.
Her mother Persis Rice had a sister Priscilla Rice who married a Francis Whipple. Priscilla and Francis had a son, Joel Whipple and another named Levi. I hope to add more sources for Joel this weekend.
I've done a bit a research in the past trying to find the connection between Whipples and Putnams because several early histories said Increase Mathews and Levi Whipple were cousins. They are both nephews to Rufus and are not blood relations. Increase is related to Rufus through his mother Huldah Putnam. Levi is a blood relative to Persis.
