Making a comprehensive claim has never raised my premiums. Comprehensive claims are generally claims that aren't your fault. Examples include rocks hitting your windshield resulting in replacement or repair, stuff falling on your vehicle while parked, and so on.
I've made a few comprehensive claims- never has it resulted in my premiums going up. I've actually been very fortunate, in my 22 years of driving (all with the same agent/insurance company), I've never been in an accident that was my fault or seen my premiums rise because of a claim- and I've had plenty of claims. My 1st car was rear-ended twice- once pretty badly, I've had two rock stars repaired, two windshields replaced, a hood replaced after a piece of concrete fell off a building and hit it, and a relatively new car totaled after someone ran a red light and t-boned me.
My rates have never been raised because of any of those claims- because none of them were my fault. Living in the city- I also have very good coverage with low deductibles and my rates are pretty good. It helps that my wife is a safe driver with no accidents on her recored either.
If you are in doubt, just call your insurance agent- and they can tell you if a comprehensive claim will raise your rates.