I have absolutely no idea how loggers work in a police environment, but
years ago the broadcast station I worked at had a stereo (2 channel)
logger.Seems to be it would be a simple matter to feed the transmit signal
to one channel and the receive signal to the other.

Otherwise, it would be a fairly simple matter to split the dispatcher
microphone signal. Take one side of the split and feed it to a 2 input
mixer. Split the receiver output and feed one side of the split to the other
input. Take the output and run it into the logger. In a real world
environment things would be a bit more complicated as you would probably
want to do some signal processing, such as audio AGC, before recording.