Is there a free site to file state taxes for two states?

If you are present in a state, then any income earned during this period, must be reported to the state.

To your resident state, you must report your worldwide income for the year. Read Your U.S. Tax Return: Working or Living in Two or More states

Some states allow you to file for free on their state tax department's website, but usually only for simple returns.

If you are filing for two separate states, by definition, your return is NOT simple.

The commercial tax software makes the big selling point of offering the federal tax return for free. However, they make it up by CHARGING for the state returns, so your chances of getting the two state returns done for free are minimal.