Paid double tax for work in another state. What should I do?

It depends. Are you commuting to Connecticut or telecommuting from New York? You will have to file a resident NYS return and all of your wages are taxed by New York. You will also have to file a nonresident Connecticut return because state taxes were withheld. 

However, where you worked (and why you telecommuted, if you did) will determine which state the income is actually sourced. 

Connecticut uses the Convenience of the Employer test in determining source income. Generally, in a state that applies this test, wages earned by a nonresident are allocated to the employer’s location unless the nonresident works from an out-of-state location due to the necessity of the employer rather than the convenience of the employee. 

If you telecommuted for your convenience, then your wages would be taxable in Connecticut. However, in that case, you will not be double-taxed because New York will give you a credit of taxes paid to another state. 

If you telecommuted for the convenience of the employer, your wages are not taxable in Connecticut. However, you would still have to file a Connecticut return to get a refund of state tax paid. 

The first thing you want to do is make sure you've filled out the Personal Info section correctly:

1. With your return open, select My Info in the left-hand menu.
2. Then, on the Personal info summary screen, scroll down to Other State Income, and select Edit.
3. At the Did you make money in any other states? question, answer Yes and make sure your nonresident state is selected from the drop-down.
4. Select Continue to return to your Personal info summary.
5. Click on State on the left hand side. 
6. Add the state of Connecticut as a non-resident, if you have not already done so.
7. Follow the on-screen instructions. 

To ensure accurate calculations, always complete the non-resident return first to ensure accurate calculations. 

Thanks.

I already put all my other information. Does it mean that I need to delete it and add non-resident info without anything else? Or I need to file non-resident first? 

No, you do not have to delete anything and you can file your two state returns and your federal return at the same time. Before you submit your returns, please ensure New York is giving you a tax of credit paid to Connecticut.

To do so, please follow the instructions below:

1. Continue through the New York return until you reach the page titled Take a Look at New York Credits and Taxes. Scroll down to Credit for Taxes Paid and click Start next to Taxes Paid to Another State.
2. Click Edit next to Connecticut on the page titled Other State Tax Credit Summary.
3. If the Portion Taxed by Connecticut is correct, click Continue.
4. If the Connecticut Tax is correct, click Continue.
5. TurboTax will let you know what your credit amount you qualify for on the following screen.

@Jenya