I worked in CT for a summer but had a permanent address in RI. I paid taxes in both. But that may just be the arrangement that RI and CT have.

Also check to see if the company you're going to work for has an office in your home state. They might be able to assign you that office as your "home" office and process your pay through there so avoid out of state stuff. By no means advocating dodging taxes, but it may be a way to simplify. Definitely would talk to a pro about it.