If you live in Trumbull, then you are hearing Troop G. in Bridgeport. The hotline is dispatched out of State Police dispatch centers for the most part. For example, around my area, I hear "New Haven to Troop I on the hotline". Then immediately, Troop I will dispatch the incident over their system . So it makes more sense when you hear someone calling into the state vs. the other way around. Monitor the frequency and you will see what I mean.
Manny is correct. As a former CSP dispatcher, we are supposed to state which troop we are calling from over the radio "hotlines" (45.8600 or the Fairfield County system). Usually if someone says "state" they are being lazy or in a rush to get the information out. 45.86 has multiple users and is utilized by all the troops.