Car insurance in the United States has a lot of peculiarities because of the way it's organized. Each state has specific regulations and legal frameworks considering car insurance, and the differences between two neighbor states can sometimes be quite significant. Starting with the minimum requirements on third party liability that differ considerably from one state to another, to specific requirements on car insurance purchase within the state. So it is often very important to know when you should switch car insurance when moving to another state.
First of all, the main requirement concerning car insurance is that you should buy a policy in the state your car is registered. And taking the fact that vehicles in the United States are registered according to owner's residence, it means that you should buy car insurance from a provider who is licensed in the state your domicile is. The notion about licensing is also very important, because not all companies work in most states of the US. Even bigger insurance providers who are covering the national markets aren't licensed to work in all 50 states of the US, and are usually operating in specific regions. So it's always important to check if a particular insurer is working in your state when checking quotes.
The moment you move to another state for residence is when you have to switch car insurance providers and policies respectively. Most insurance providers usually require you to notify them about canceling your policy within 30 days after you have moved to another state. So make sure to inform your agent or broker about changing residence in order to make sure they have the time to terminate your policy with the provider.
But not always you have to switch policies when going to another state. It all depends on the move itself. If you're moving permanently and changing your residence for good, then you will have to switch providers and states. However, if it's temporary move (contract work, college, temporary stay, etc.) then you typically don't have to switch providers, as you will have to switch back when you return home. Consult with your insurance agent about the formalities of temporary move to another state in the state of your residence and act accordingly. However, the most important thing you will have to keep in mind is avoiding lapse in insurance coverage, since it's quite dangerous to drive the roads without proper car insurance coverage.