Your first step is to contact your local police department and speak with them about the threatening emails. Bring them with you when you go to the police or have them available if an officer comes to your home. You can also contact an attorney to advise whether you can file a civil suit. You may also be able to get a temporary restraining order (TRO) or a Peace Order (depending on your jurisdiction) to prevent contact.
It sounds very serious to me and that is how I would approach it. That being the case, you need to immediately contact the police and advise them of your situation and follow their advice.
No information provided in response to these questions can be relied upon in any way without further personally consulting with Attorney Kerrigan and Attorney Kerrigan consulting personally with you regarding your specific legal situation.