Correct. Connecticut will give you a credit for your state tax liability for income earned in another state, and that is based on 2016 income only. Your comments state that the $300 was for your 2015 tax liability. That amount could be a credit for you 2015 Connecticut return, but is not a credit for your 2016 return. Since your 2016 NY tax liability is zero, Connecticut has no tax credit to provide, since you are not paying tax to NY this year.
Having said this, if you have a credit that could have been applied in 2015 and wasn't, then you may amend the 2015 return to claim that credit. In general, your credit is based on your tax withheld, minus the state refund or plus the tax amount due. That $300 should have been added to whatever tax amount you had paid in already. If it wasn't, it is possible (but not a guarantee) that some or all of that amount may be refunded for credit that was not applied originally.
Here's an FAQ to assist you to amend the 2015 return if you choose to do so: https://ttlc.intuit.com/replies/3288565
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