Your car is only regulated by where you have it registered. So, if you are in Tennessee as an example, Davidson Co residents pay higher plate fee and also must pass inspection. Residents in Rutherford Co pay a slightly lower plate fee and no longer have to pass inspection. Inspections in the US are largely emissions. Some counties have dropped this because they found it ineffective or not cost efficient.
If your vehicle doesn't meet obvious road standards, you'll simply be pulled over and ticketed.