How can I find out if my local taxes were filed this year. H&R block did them and can't find info pertaining to it

You should have copies of this... its not even been two months since they have required all W-2 to be mailed by. You would have had an appointment and taken them in if you had them done.

You are rquired to retain them for at least 3 years by the IRS... you can't rely on someone else to do it in case of an audit.