What does "chasing leads or chasing tail" mean?

A "lead", in the context of a detective story, means something or someone who can help you get closer to finding the truth about a case. Chasing leads means he is looking for people or things that he can use to solve his case.

"Tail" refers to an "ass" (as in a butt), particularly the ass of a sexually attractive woman. Chasing tail means that he is looking for someone to have sex with.

This quote is a cute way to say this detective is spending part of his time working on his case, and part of his time looking for sex.

Chasing Tail means a person assigned or employed to follow and report on someone else's movements and actions

No. Chasing tail refers to someone looking for sex. Your definition is more apt for someone who is 'tailing' someone (following them).

If you think the person assigned to follow and report on you has a nice ass...

Would that be "chasing your own tail"?

How about a direct, contextual quote?

...Good thinking!

That is really helpful. Thank you!