The police is chasing somebody on:

1. TV show, the police chase the person down until they are arrested, even if it takes the entire force to do so.

2. movie from the police perspective, the person gets away, but the police take a shortcut and catch up to said person. They might also wait and get the person later when person least expects it.

3. movie from persons perspective, they get away, usually because the police crashed their car.