Legal Question in Criminal Law in California

Re: death threat

To be a criminal threat a statement must be directed at or communicated to the supposed target. A letter from your client to a third party would not qualify.

It also seems unlikely that the doctor actually intends to harm you. When people say things like this they are usually speaking figuratively.

If you have reason to think the doctor means what he said, then by all means report it to the police. They may be able to intervene even though no crime has yet been committed. But don't make such a report merely to gain leverage in a business dispute or for any other ulterior purpose.