You are a part-year resident of each state. For the year that you moved you will have to file a part-year resident tax return for each state, assuming that both states have state income tax. You will pay tax to each state on the income that you earned while you lived and worked in that state. Check your pay stub to make sure your employer is withholding tax for the correct state.
I am assuming that you worked in the same state that you lived in, both before and after you moved. If that's not true, post details.
Owning a home in another state that you don't live in makes no difference. However, if you rent out your home in the old state, that is income from that state, which adds complications. If you are renting out your old home, post details.
Also note that if you sell your old home more than three years after you moved, you will lose part or all of the exclusion of gain from selling the home.
