I have seen a few different configurations and antennas used.
800mhz wise some cars have roof mount NMOs, most have them in the trunklid.
I have seen three different styles of Antennas.
Quarter wave chrome nut.
3DB Colinear antenna, Mostly the Motorola model.
Low profile Antenex Phantom antenna. (The Impala cars all seem to have these)
For other antennas
The traffic arm of IMPD often has CB Antennas used with CB Radios.
There are also the aforementioned trunklip mounted NMO VHF sticks often used with illegal tac radios.
There are legitimate IMPD ham operators as well....
Then there are the unusual..... I -swear- i saw an IMPD cruiser with a split ball quarter panel full lowband quarter wave antenna. LOL... someone serious about CB?
someone should start a discussion about all those Antennas on Indiana State Police cars.... they have so many it looks like a porcupine...