How do police/ambulance helicopters communicate with ATC? I was watching some police programme on TV the other day, with an air chase that had the police helicopter crew on their toes; having to perform a lot of sudden maneuvers.

How do police, or HEMS (medical), helicopters communicate with ATC? I presume they get priority, but do ATC clear other traffic out of the way? Is there a comms person/navigator on-board? Do they simply "see and avoid"?
The exact procedures will vary locally but typically ATC will give priority to police and ambulance helicopters that operate emergency services. 

If these helicopters are operating in controlled airspace, communication with ATC will be done by normal VHF radio. There is no need for a dedicated communications person, the pilot will be in contact with ATC.

Sudden manoeuvring of these flights is rarely a problem for ATC since these aircraft are operating under Visual Flight Rules. 

When chasing a car, the pilot remains responsible for keeping clear of obstacles and other traffic, therefore this requires a second person to keep a look out (either on the car or the surroundings)