My Federal W2 reads Total State for Employer's State ID and box 15 is blank. But the State W2 reads the state and the Employer's ID. How do I enter this?

Don't enter them as separate W2s.  Enter it all on 1 W2.

If the EIN number is the same and you work in more than 1 state or city, sometimes they will give you another W2 with the extra state information on it and the top part the same or not filled in.  If this is the case, list one W-2 but include both state or local  taxes on it.  It will let you type in more than one line for boxes 15-20.  Don't add the boxes together.  

The EIN number on the W2's are the same, but the Wage are different amounts.  The Employer address is Big Lots Company 4900 E Dublin Granville Road Columbus OH  43081 on the 1st W2 and on the 2nd W2 it is also Big Lots Company Agent for CS Ross company 4900 E Dublin Granville Road Columbus OH  43081.  I haven't been able to find out why I am receiving 2 W's as I no longer work for Big Lots.  We did move to a new building but it is in the same town.  That is the only reason I could think of for 2 W2's.  I do appreciate your previous answer.  Thank you.

If the wages in box are different then you need to ask Big Lots why.  Do they both have your ssn on them?

Yes they do have same SS#.

We changed payroll systems during the year do you think that could be the reason for receiving 2 W2's?  I will contact Big Lots to see if I can get a answer.  Thank you for your help.