Maybe......
This depends on WHICH "Police Positive" you have.
Colt had two revolvers of the same design, one the "Police Positive", the other the "Police Positive Special".
The Police Positive was built to shoot short, now obsolete cartridges like the old .32 S&W and .38 S&W.
Colt didn't want the S&W name on Colt pistols so they just changed the bullet shape slightly and sold the ammo as the Colt .32 New Police and Colt .38 New Police.
The S&W and Colt versions were totally interchangeable.
The Colt Police Positive Special was made with a longer cylinder and frame so it could shoot longer cartridges like the .38 Special.
If you have an actual Colt Police Positive, you cannot shoot the same .38 Special ammo as the S&W 642 or Detective Special.
The cylinder will be too short to chamber the longer .38 Special, and the barrel was bored for the larger .38 S&W cartridge.
Check the barrel on the Colt.
If it says "Colt Police Positive", then ".38 Special" it's a Colt Police Positive Special made for the .38 Special.
If it says "Police Positive" and ".38 Caliber", it's a Police Positive and chambered for the .38 S&W/.38 New Police.
Also, compare the frame and cylinder of your Detective Special to the Police Positive.
If the frame and cylinder of the Police Positive are noticeably shorter, it's a .38 S&W/.38 New Police.
The .38 S&W/Colt New Police is still sold by a few ammo makers.