As a rule of thumb, (almost) every bridge is state maintained. Also see https://gis.massdot.state.ma.us/StateHighwayLayoutsOn a side note, I really wish jurisdiction over the bridge was better established, cause there's this one awful expansion joint on the Boston-bound side that is, and has always been, a (literal) pain in the ass to bike over, and I have no idea who to gripe to. :/
Not 100% accurate but pretty decent.
Zooming in on Mass Ave, l would assume state jurisdiction actually extends until Back street to include the Storrow overpasses rather than ending at the Southern dry pier, but maybe Boston actually owns two spans, who knows.