You should file an extension if you do not have all of your forms needed to file. The 1099-G definitely needs to be included on your tax return. You can contact your state and have a copy sent or emailed to you.
How
do I file an IRS extension (Form 4868) in TurboTax Online?Technically, you can file, but you will eventually have to add it to your tax return and that will require amending which is something you want to avoid.