For starters, understand that anything with a motor in it, starts losing value the day you start that motor up for the first time and drive it off the lot.
Next, the interest rate on the purchase of a new car, will always be lower than that for a used car. But the way the market has fluctuated recently, it is possible over time for the used car interest rate, to be lower than the new car interest rate you may have agreed to years ago. Though I doubt that in today's climate.
If you purchased the car new originally, when you refinance it, it's no longer new. It's a used car now. So I would fully expect the interest rate to be at least one point higher, if not more. That would be regardless of what your credit score may be.
If you purchased the car new say, 5 years ago and someone is offering you to refi with a lower interest rate, then either the original financier of the car sucked you into a higher rate above the market average (maybe because of your credit score?) or the entity offering you the lower rate now, has yet to inform you of "the catch", whatever that catch may be.