I live and work in CT but my employer is based in Ohio. My w2 doesn't have a CT employer tax ID number. What do I do?

No problem. You don't have to enter any CT wages because you live there. Everything is taxed by CT as a resident. 

Your resident state taxes all income but gives a credit for income taxed by another state.  Please carefully follow these directions.

You will need to prepare the states in a special order. You may need to delete both states and begin again.

1. First, prepare your non-resident OH return. This creates your tax liability for the non-resident state. How do I file a nonresident state return?
2. THEN prepare your resident state CT return and it will generate a credit for your income already being taxed in the non-resident state.
3. The credit will be the lower of the state tax liabilities on the same income. You may owe your resident state.

It isn't possible for the program to create a credit before it knows the liability. Your returns may be wrong if you do not prepare the states in this order.