Legal Question in Business Law in California

You cannot legally do so.

Don't record with letting them know beforehand you may record the call.

Probably not - see Penal Code section 632 which prohibits recording any telephone communication which a party reasonably believes is confidential. However, there may be a point at which the caller no longer has a reasonable expectation of confidentiality. If threats are made, for example, the caller probably could no longer reasonably expect the threats would go unreported; hence, the expectation of privacy would go away the recording would no longer be unlawful under the statute. Note that making an obscene or threatening telephone call with intent to annoy is also criminal (see Penal Code section 653m).

The general rule is NO, as indicated by others above, BUT an exception exists if you can show you are doing so for the purpose of documenting a crime. Phone threats and harassment are a crime. Contact the local police to report the crime and listen to their advice about recording or not. If this is something that justifies filing a civil lawsuit or restraining order, feel free to contact me for legal help.