I've never seen an apartment application create a hard inquiry on my credit report, but I have seen one when switching to a new insurance carrier. I've also seen them when getting a savings or checking account. You should not see a hard inquiry from "shopping around", but when you actually settle with an insurance carrier they WILL check your credit as all insurance agencies that I know of use your credit score when determining your insurance rate. The lower the score, the more the car insurance is going to cost you. Regardless, they cannot pull your report without your permission so ask them when you are getting quotes if they are going to pull your report or not. If so, it's up to you if you want them to do it or not. They can't give you an exact quote without it, but they should be able to get in the ballpark.