Can I file my state taxes and get an extension on my federal taxes?

No.  State income tax returns use the information from your federal income tax return and state's require a copy of your federal return to be included with your state income tax return filing therefore you will need to file your federal income tax return in order to be able to file your state tax return.

If you need more time to file your federal taxes, you will want to file an extension for your state also.

Many states give an automatic extension when you file the federal extension Form 4868 but check with your state's Department of Revenue to make sure that your state doesn't have a separate state extension filing. Here is a link to the State Department of Revenue Contacts