A couple of years ago I had to have my water heater replaced. Because the home was under a warranty at the time, it was cheaper to have a contractor do it instead of doing it myself.
When the contractor was finished with the work, he said he would email me the contact information and permit information so I could call the county and have an inspection.

In the midst of COVID, and because I generally don't invite the man into my house unless needed (which is never), I forgot all about it.

Jump forward to this past week, I get an email from the contractor (it's larger than a mom-and-pop business) that my permit is about to expire and I need to call the county for the inspection. They even attached the notice they got from the county. The email says they (the contractor) won't be responsible for having to pay for a new permit.

So my question is this: what happens if I don't call and get the inspection? Civil penalties, fines, they shoot my dogs, or...?

I can't find this answered in MN statute anywhere, so if you know the statutory reference, extra bonus points to you.

By the way, I live in a small town where the ordinance says they just follow county building code, and the county follows state code.

Thanks in advance.

ETA: my HVAC system is going to need replacing within a year or two, at most. If I don't get the water heater inspected, I'm assuming the county can jam me up on the permit for the HVAC, correct?

tagging for interest in the answer.  I'm in Ramsey county and had my water heater replaced by a plumbing company in Nov 2020.  I don't even recall anything about a permit.  There might have been one, and if there was one, I am 110% no inspector came to my house as I was here all day.  Though I can see where this might be a county by county thing.

The only thing I can think of, if you never get the inspection, is that it would probably be a good idea to disclose it when you sell the house someday.  I'm usually the kind of guy that wants to say fuck it to those kind of things, but I wouldn't want it coming back to bite me in the ass either.  When I sold my prior home I made sure to declare that the sewer line backed up once while washing clothes due to roots and that it had been augured out.

Agreed about the disclosure. Last house I was in I replaced the water heater. It was a pain in the ass but I learned a lot and would have done it again.

I disclosed everything that was done to that house (and I did quite a bit), because I didn't want that coming back to haunt me. I'll do the same here, when I retire and move to a more free and less taxed state.

If it's a gas heater, probably want to make sure it's vented properly.  Combustion gases can kill you if not.  
If electric, probably want to make sure the proper sized wire was used, and it's wired properly.