IRS Form 4868 is what you will be looking for. It can be filed electronically or mailed in. Either must be done on or before April 15th to be valid. The form asks for an estimate of the 2014 tax liability and the 2014 payments (generally the withholding from W2s and any estimated tax payments). Then if there is any balance due, submit a check with the extension form.
So the difficult part is really determining the tax liability without actually preparing the tax return. Obviously if you had time to do the return, you wouldn’t be filing an extension!!!! One possible option is to use the prior year tax liability, then consider any major changes that might have happened during the year. If 2014 was pretty much the same as 2013, then last year’s tax liability could be a pretty good estimate to use.
Michigan will accepted the Federal extension, so you will not need to do a separate extension for the state. However, if you were able to finish your Federal return, but did not finish your Michigan return in time, there is a MI 4868 form that can be filed so that you can get an extension to file for your MI return itself.
Remember, this is an extension of TIME. So any tax owed when you ultimately file your return will be subject to interest owed for each day late after April 15th. That’s way it is important to pay any balance due determined when you file the extension form. What this form does avoid, and this is really helpful, is the failure to file penalties. And it’s always nice to keep a few extra bucks in YOUR pocket.