Yes. You can do anything you want in your state. If you live near a state line, like I do, you can do business in the other state too in the area just over the line. This falls under the fair trade between states act. You still must register with their health dept, and if their requirements are similar, all is well. They can inspect your kitchen at will, just like your local health dept.
I need to add something. My brother-in-law owns a restaurant in the next county where health dept regulations are very lax. When he wanted to give away hamburgers and hot dogs at his mother's store (in my county)during a festival, he found that even though he had a license in another county, he had to abide by this county's rules... running water on site (a parking lot), and a few other sanitation requirements, which made it impossible. But, he could fully cook his food in his county and reheat it here. So, if you have a situation like this that involves preparation off-site, check first.