Yes. In fact, you don't even have to live there. Also, if your business is an LLC or a Corporation etc. registered in one state and doing business in another state, you may need to register your business in the other state to allow your "foreign" company to do business there. Also, you may have to file franchise, employment or other taxes in the other state depending on your circumstances, ie. having an office, employees, assets, locally taxable sales etc. in the other state.
Probably.
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