If I worked in two states do I file two separate tax returns

You may have to file two separate state returns. Every state has different rules. Each has a filing requirement based on whether you are a resident, part-year resident or non-resident and how much money you made.

Some neighboring states have agreements such as credits for taxes paid to another state and reciprocity. You would need to go to the Department of Revenue for your particular states to see what they require.

Please see this LINK for instructions to reach each DOR.

It depends on the states and type of income (W-2 wages or self employment) and state of residence.

 The general rule is: your report all your income on your home state return, even the income earned out of state. You file a non-resident state return for the state you worked in and pay tax to that state. Your home state will give you a credit, or partial credit, for what you paid the non-resident state.  But there are exceptions.