Does teeth crowning require anesthesia?

Just local: No need for anything more. I find that giving only what is needed and thereby decreasing risk by not adding more drugs is the safest way to practice.

Good idea: I assume you are talking about local anesthesia, that is, "novocaine". It is never required, but it usually recommended so the procedure doesn't hurt. If you are getting dentistry on a tooth that has had root canal therapy, the dentist might be able to drill the tooth without novocaine and without causing any pain, depending on where the end of the crown is. Below the gum will hurt.

Crown and anesthesia: Preparing a tooth generally require local anesthesia unless the tooth has root canal and the crown margin is going to be prepared above the gum-line.

Local anesthesia: This can usually be done with just a local anesthetic. Talk to your dentist if you have questions or concerns.