I was told that Wyoming residents qualified for a refund of the healthcare penalty for 2016 and 2017 but how do I find any information on this or how to file for this?

[Zbucklyo]

I think you were told incorrectly.  Why would Wyoming residents be treated differently than anyone else?  Also, Wyoming has no state income tax, so I don't see any way for a deduction or credit to be given.

[caleb.monk]

It's because the marketplace in Wyoming did not provide options for people to sign up for healthcare - there were basically two options only- so it supposedly is a return of the federal penalty, because we wouldn't have paid a state penalty just the federal one.

[Zbucklyo]

There is a hardship exception that might apply if there was only one insurance option available in your area, but that doesn't apply to Wyoming specifically.  It is not a refund of the penalty; but the penalty is waived under certain circumstances.  You would apply for the waiver when filling out your healthcare information in the federal interview.