If I just filed my extension for federal tax will Utah State tax automatically be notified? Do I have to file a separate extension for the state?

You will need to file separately.  Utah (UT) automatically gives you a 6-month extension to October 15. If you owe, submit payment by April 15 to avoid penalties. You can either mail a check with Form TC-546 or pay online through their Taxpayer Access Point site.

Please see updated answer.

Some states will piggyback on your federal extension, others require a separate filing.

https://ttlc.intuit.com/replies/7400057

Please see this article from the IRS:
https://www.irs.com/articles/state-tax-extension-information