Prior to 1896, there was no standard revolver issued th the NYPD. Roosevelt was chair of the board of commissioners, and appointed a committee to find the most appropriate gun for the job. Remember, by then he had served as a sheriff out west, so had some law enforcement experience. As a result of their tests, they (and he) chose the .32 Colt New Police. Teddy ordered 4,500 of them for the department. Here is a link to a nice story, with some really great photos, and some contemporary news articles:
Colt Pistols and Revolvers for Firearms Collectors - New Police .32
I'm not saying that this would be a viable choice for today's world, but it was a step towards bringing uniformity to the arming of the police. He also mandated training, and worked to eliminate police corruption, which was rampant prior to his tenure there.
Best Regards, Les