>>>around here, contractors hate to get permits and often tell the owner to do it - unlike what Curt E. describes for where he is, the law requires a permit but does not require the contractor to get one...<<<
Oregon uses the same Code as Michigan (as well as most other states these days) - all based on the International Mechanical Code. The Code (in fact, all Codes I've ever seen in 30 years) require a permit by the "owner, authorized agent or contractor". A contractor doing work without a permit is in violation of the building code - it is his obligation under his license to see that a permit is pulled before he does work. If he can talk some dupe homeowner into doing it for him, good for him.
As I stated, the only reason a contractor would ask the homeowner to pull the permit is because he doesn't have a license (a homeowner can do his own work without a license) or he wants to shirttail onto the homeowners GL insurance. Pulling a permit yourself for work being done by a contractor you hire enters you into a General Contractor/subcontractor relationship. That is a recipe for trouble. Let the contractor do everything, then you'll only have one phone call to make when the house blows up