Actually there where 4 different manufacturers called Bay State (5 if you count also the car sold under the Walkins brand)
The more important were the Boston's one, active from 1907 till 1908 and the Farmingham's one, both from Massachusetts, from 1922 till 1926, that is the one of the puzzle. There were two models available: the Model 1, a 6-cylinder 58hp, 121" wheelbase sold in 6 differen bodystyles and the Model 2, 6-cylinder, 60hp 121" wheelbase, available in the same 6 bodystiles.