Can my boss search my desk and copy personal documents I keep in it?

Your boss may have a right to search your desk depending on why he feels he must do so, and how your office is set up.  If the documents you have are truly personal, then he could not copy them.  But it depends on what these documents are. You should meet with an attorney to explore this in more detail

Generally, if the Boss supplies you with the desk, and it is located on the boss's premises, it isn't your desk, but it is the Boss's desk. You do not have a reasonable expectation of privacy in what is in or on your desk. Thus he can inspect and copy what is there (generally).  There are exceptions, of course. Your medical information is highly private and you have a reasonable expectation that the boss will not expect or copy such records. Privacy laws always start with determining the circumstances in which a plaintiff has a reasonable expectation of privacy.  It depends on where the papers are, what the nature of the papers is, and the circumstances that might lead you to believe you had an expectation that the papers would not be subject to inspection a]nd copying by your employer.