Same-sex marriage became legal in Minnesota on August 1. Effective with 2013 tax returns, same-sex married couples who file Minnesota tax returns will be required to file those returns as married. This will apply to Minnesota residents and to non-residents required to file a Minnesota tax return
From the Minnesota Department of Revenue news release:
Minnesota will treat all married couples the same for tax purposes, including income and gift and estate taxes, employee benefits, contributing to an IRA and claiming the earned income tax credit or child tax credit.
If you are required to file a Minnesota income tax return, then you must file that return using the same filing status you use for your federal income tax return.
For non-residents and part-year residents, if only one spouse is required to file a Minnesota return and you file a joint federal return, you must file a joint Minnesota return.
You are considered married for the whole year if on the last day of your tax year, you and your spouse are legally married.
Same-sex married spouses who have changes to exemptions, adjustments, deductions, or credits may want to give employers a new form W-4 to change withholding status or number of allowances.
Estate and Income Tax forms and instructions for tax year 2013 will apply to all taxpayers.
Minnesota state tax laws applicable to married persons do not apply to registered domestic partners, civil unions, or other similar relationships that are not considered marriage under the federal ruling.
Additionally, if a couple in a same-sex marriage amends a prior-year federal tax return to file as married, they must also file an amended Minnesota tax return as well.
You can find the news release from the Department here.