No. She would not recover all the taxes paid to Connecticut. Connecticut and New York do not have reciprocity. She should file a nonresident Connecticut tax return, as she has a tax liability to Connecticut because she earns money there. She may have a refund if she overpaid, but she is not simply exempt from tax.
On your New York State return, she'll get a credit for some or all of the taxes paid to Connecticut. This will help minimize double taxation.
Your wife may be better of filing a separate return with Connecticut. If she chooses to do this, you will be better off creating a second username for this return. If you are filing a joint federal return, prepare a "mock"/pretend Married Filing Separate federal return for your wife and transmit just the Connecticut return that way. Do not file the pretend MFS federal return.
On your joint NY return, you would enter the tax liability on the Connecticut return. You will need to print the CT return so it can be referenced during this process.
If you are filing a joint federal return and do not create a second username for this CT return, the CT return will also be a joint return. This may cause you to overpay CT tax.
