epa 608 and hvac contractor license is the requirement for the freon like I said. That's nation wide.
You could pull the owner-builder permit usually, you just can't physically buy the materials you needed, and thats why the permitting office might add that. Obviously I can't know how every locality is but usually. That said, you're probably in Denver. I know they do dumb stuff like that.
If you talk to them, you can explain that you plan to subcontract that part out.
That said, for repair/replacement 90% of ACs across the country are not permitted by small HVAC businesses for residential. Half of it is a money grab by the town, but there's no way to really verify that it's a replacement unit. A home inspectors don't know sh** about fu**.
New construction is different, since you have phases of inspections for different trades. Though it's nice to have inspections to verify the minimum has been done, unless the inspector was a prior HVAC guy, high probability he just looks at wants on the sheet, shrugs, and checks off everything. He ain't going to check your capacitors, your manifold numbers and emissions or your low voltage wiring.
He might go in and check to see if it's blowing cold and walk away. Haha