State tax filing

Are you referring to the Renters Property Tax Refund?   Did you prepare and print out the Form M1PR with TurboTax and mailed it with a copy of your CRP to the address on your M1PR form?

You can use this tool to check on it periodically.   Under "return type" indicate property tax refund.
<a rel="nofollow" target="_blank" href="https://www.mndor.state.mn.us/tp/refund/home">https://www.mndor.state.mn.us/tp/refund/home</a>