Tenant refused to move and threatening lawyer

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I’m not sure where to start with this person.  

They refused to give proper written notice at the end of their annual lease to say whether they were staying or going to depart.  Verbally they stated they were departing. 

So we set up move out and started taking appointments and applications (luckily I didn’t run any yet). 

Now they say they aren’t moving and have since not moved out.  Won’t give a timeframe for when they will move and won’t sign anything.  

Do I just go while he’s paying (I don’t typically do month to month)  and just one day they will be gone and I’ll move new tenants in?   My concern is they just chuck the annoying threats of ill have my lawyer contact you.  I’m not worried about some lawsuit or something.  

So do I send notice of nonrenewal and a move out date or just be happy they are paying and collect rent and stop stressing. Thanks