New Mexico recognizes and accepts an IRS automatic extension of time to file. If you obtained the federal three-month automatic extension by filing federal Form 4868, Application for Automatic Extension of Time to File U.S. Individual Income Tax Return for tax year 2019, you have until October 15, 2020 to file your New Mexico return.
To extend your deadline beyond the three months, you are required to obtain an additional extension through the IRS or the state.
Note that this is an extension of time to file, not an extension to pay any tax due.