Another way to look at it is this is vestigial signage, predating the work on the Oak St Connector & (potential) truncation of the route. Could be that the state is not concerned with removing signs from city-maintained streets, and the city's not too fussed about it either.
FWIW, here's a sign on the connector itself, the state-maintained bit, removed between
Oct 2016 and
Jul 2017.
The rationale for for the truncation was discussed in the
freeways missing from usasf topic:
Look closely at the state highway map and you will notice that maintenance of the one-way pair of surface streets east of CT 10 has been turned back over to the city of New Haven (as they wanted). What remains of the Oak Street connector is still officially designated CT 34, but is disconnected from the rest.
Signage for CT 34 was deliberately removed from I-91/95 in this area and added to signage for exit 44, because ConnDOT (and the city of New Haven) wants traffic heading to CT 34 west to go that way rather than cutting through downtown.
I do suppose it remains to be seen whether The remaining Oak Street Connector will get redesignated as SR 7xx or whether the status quo of "it sort of is and sort of isn't" CT 34 will remain basically forever.
A maddening gray area to be sure.