Your auto insurance rates will not necessarily be raised because you are paid out for a comprehensive claim due to your car being stolen. Typically, when you have a comprehensive claim, your insurance carrier recognizes that it is normally due to something that is not your fault, and you had no control over, (i.e. theft, vandalism, hail damage, etc.) and do not raise rates.
State laws and insurance company guidelines do differ though so check with your insurance agent to find out for certain if your premiums could go up. Your agent should be able to explain your provider's rating system to you. It could be that this one claim will not cause your rates to go up but if you have had a lot of claims made in total against your policy then your claims activity could cause an overall rating increase.
If your rates do go up, it may be time to start shopping around for a new insurance provider. You can start car insurance comparison shopping here with us.