My interpretation is that in Minnesota, the landlord of a residence is responsible for keeping the smoke detector functioning, and that this is part of the implied warranty of habitability. I think that means that if a fire breaks out due to a failure to install or repair the smoke detector, the landlord is liable for damages.
I think the most relevant laws are these 504B.161 COVENANTS OF LANDLORD OR LICENSOR Subd 1(a)(1) and Subd 1(a)(2) and Subd 2 and 299F.362 SMOKE DETECTOR; INSTALLATION; RULES; PENALTY Subd 5 and 5a.
But I know in the law there's often more to the story. Is there a way for a tenant to agree to assume the risks resulting from broken smoke detectors? What happens to a lease that tries to do this?