You will need to file a part year MN return for the time you lived and received income in MN. TX has no state income tax. Moving expenses are not deductible on a federal tax return, unless you are a member of the military.
https://ttlc.intuit.com/questions/1901227-how-do-i-file-a-part-year-state-return
https://ttlc.intuit.com/questions/1901560-how-do-i-file-if-i-moved-to-a-different-state-last-year
https://ttlc.intuit.com/questions/1901267-which-states-don-t-have-income-tax
Per the tax laws that changed for 2018 and beyond, moving expenses are not deductible on a federal return except for certain active duty members of the military.
There are several states that allow a deduction for moving expenses on the state return: AZ, AR, CA, HI, IA, MA, MN, NJ, NY, PA and VA You can enter your moving expenses in the federal software and the information will flow to your state return.
Go to Federal>Deductions and Credits>Other Deductions and Credits>Moving Expenses
Hi Andurain
In addition to the answer already given, I'd like to add my thoughts:
Since you moved from Minnesota (a state with income tax) to Texas (a state without income tax), you'll need to file a part-year resident return for Minnesota no return is needed for Texas.
Unfortunately, due to the Tax Cuts and Jobs Act, moving expenses are no longer deductible for most taxpayers for tax years 2018-2025. However, if you're an active-duty military member who moved due to a permanent change of station, you may still be able to claim moving expenses.
Have a Great year!