If my tenants had a month-to-month lease and I gave them a 45 day notice to leave but now they are refusing to pay the last month's rent, what can I do?

As a landlord in Minnesota, you can choose to accept the security or damage deposit in place of the last months rent, but you do not have to.

Easiest solution would be to wait until they move out and file a conciliation court claim.  I say wait because you want them out as quickly and quietly as possible without them destroying your place.

Conversly, you can always move to evict, but by time its all said and done, the lease will most likely be up by then.

Never resort to changing the locks.