Will your premium go up if you file a claim on your comprehensive auto insurance policy?

It really depends on the circumstances of the claim, and if you were At Fault.

If you were at fault, and you need to use your comprehensive/collision to pay for your damages you probably will be looking at a noticeable increase unless you are over 35 and have never had an accident it may only go up by a few dollars here and there.

If you weren't at fault but require the use of your coverage to pay for your own damages because the other person had no insurance depending on the severity you MAY be looking at an increase but depending on how much coverage you elected or how high your deductible is it may not increase.

Like I said it varies from case to case and rules, regulations are a fluid thing often bent and not followed up with. There's no definite for every scenario. Hope this helps.