One issue here may be the different transmitting towers. I believe the fire department uses a large tower on Plain Hill Rd, which is about 350 feet above sea level, while I believe the police depts antenna is on top of public works building with limited height.
The City Fire Department, which covers a much smaller area than the police, operates on high band with a repeater system. As far as I know, there have not been issues with it. That system has been in use since the early 90s.
The volunteer departments operate on low band but they also use the tower on Plain Hill Rd. I haven't heard of too many problems with that.
Talking between departments, police and fire, utilities, public works was discouraged in the past. Only the fire departments will share frequencies together.
I really have very little knowledge of newer radio systems today. But I do think it is possible for the Norwich Police to update their system without any type of expensive new system. Actually, this issue could have been taken care of years ago when the FD went to high band and a new central 911 dispatch was put into place.
I worked in Norwich in the 70 & 80's for Professional Ambulance. We used VHF high and and had good coverage throughout the city with mobile radios on high power. Our base was located in the hill in Uncasville CT across from the Mohegan Casino. It covered all of eastern CT and into RI.
The city should have switched to vhf high years ago. They have done it in a piece meal approach trying to save money. The City FD is the only dept to do it right. The Volunteers didn't want change and the police are appear to just not want to spend any money. I think they need a good consultant and need to listen to them. A good multi site trunk system on UHF or 700/800 would work well there. CSERN might be an option.