Was there a 21st precinct in New York City?

There was no 21st Precinct Station in NYC. There was (and is) a 20th and 22nd, but no 21st. It was precisely because there was no 21st Precinct in real life that Sidney Kingsley set his stage play DETECTIVE STORY in the detective squadroom of the 21st Precinct, and that the radio drama, 21ST PRECINCT, WA set there.

If you like West Side Story, the police were from the 21st Precienct.