The major problem in fitting grips to the Police Positive is there's actually several versions of the firearm. It was made from turn of the century to the late 1990's off and on. The result is all polpos grips are not created equal.
The grip frame itself went from a square butt design, to a round butt, to a shorter round butt. They are basically the same as the other "D" frames of their contemporaries, as Colt wasn't about to make a special frame.
Pachmayer makes grips for all but the oldest guns. These fill your hand quite well. If your frame is a later one (rounded butt, and sometimes you can only tell with the grips off because Colt made square butt grips for the round butt frame). You're choices are more. The Colt Diamondback is basically a Police Positive with adjustible sights, vet rib and barrel under-lug. While the grips aren't huge compared to a S&W "N" frame, they are much bigger than the stock polpos/detective special grips.
If you have stock grips that seem to fit oddly, like way too thin at the top, and just barely OK at the bottom, another option is a Tyler-T grip adapter. This fills in the space behind the trigger guard and really makes a big difference in the grip. They feel odd at first, but once you get used to it, it's not bad.
If your frame is the short grip type (or even the long one that's round), you can use a Barami Hip grip. The intention of the Barami is to give you a holsterless carry opiton, but it fills the hand quite nicely, without giveing you a too-fat grip. It's stock profile, except on the top right there is a built up area that as a "finger" that extends out, creating a sort of clip to be used to hook on your trousers. OK, my descriptions really doens't do it justice, as they are recongnized by many experts as worthwile to use, and I've used on for the last three years on my Dettective Special with great results. Anyway the built-up area provides a better grip, and it's a VERY comfortable grip.
In the '50's there were many aftermarket grips available in all shapes and sizes. While there may be some looking involved, they usually are dirt cheap because they are "too retro" if you know what I mean.
Any idea when your's was made? If you wish, you can IM me the serial number and I can look up when it was made. What kinda frame does it have? Once we know that, we can narrow down the choices some.
No matter what, the Police Positive has been around so long that this is certainly not the frist time someone has had this problem. There has also been a solution already made for you, you just need to figure out what it is.
Ross