Do I need to change car insurance?
Probably not.
If you're curious, you should probably talk with your insurance agent/company. It would really suck if you didn't change your insurance then found out that you needed to after the collision.
While you're talking to them, ask about renter's insurance, too.
Do I need to change car insurance?
I don't think so.
You will have to notify your insurers of your change of address so they'll let you know about it right then.
If they try raising your price consider shopping around before you go for it.
Prices vary from relatively little money to a lot of money.
If you need, here's one from my bookmarks:
http://www.quick-car-insurance-compariso鈥?/a>
you fill a form and get back prices from a bunch of carriers, it saves lots of hassle, there'll be more in Google, look for comparison sites they are free to do so it pays to shop around as prices vary quite a lot for the same policy.