There is no relation between the two resources other then you will hear the Town of Fishkill units on those channels. If Town of Fishkill Police receive a direct call to their agency they will dispatch their units on the "Base 6" talkgroup on the EDACS system. If 911 received the call they will poll for the closest police unit, and whatever unit that answers the poll is closest they will assign and turn that call over to the appropriate agency.
This doesn't apply normally for the City and, Town of Poughkeepsie and, the City of Beacon. 911 will automatically transfer those calls to those police agencies.