California tax credit doesn't affect NYC taxes?

[rtang4]

This year, I interned in California, but my main place of residency was in New York City. I have already filed my California state tax returns, where I am getting a refund of around 1000. I am also aware that since it was only an internship and my residency was still New York, I need to report those wages to both New York State and New York City. I have already paid taxes in California, and to prevent being double taxed, I expected credit from California to cover my NY taxes. The problem is, while it does cover New York State tax, California tax credit doesn't seem eligible to cover New York City tax... why is that? 

My example--

Total tax in California was 1.6k, got ~1.5k tax refund after my total payments was 3k

When filing my NY state tax returns, I owe 1.1k to NYS and 600 to NYC. My total tax in California covered my NYS taxes, but I still need to pay 600 for the NYC taxes. 

Even though I already paid taxes working in California, am I paying even more taxes (even though I shouldn't be double-taxed) simply because my residence was in NYC? 

[rjs]

If you are a New York resident and a California nonresident you don't get credit from California for your New York tax. You get credit from New York for part or all of the tax that you paid to California. A refund is not the same as a credit.

Did you prepare both your California and New York tax returns in TurboTax? There should be a credit on your New York tax return for part or all of the tax that you paid to California. It's called the Resident Credit. It's on Form IT-201 line 41, and there should be a Form IT-112-R included in your New York tax return to calculate the credit. In the TurboTax interview for New York, on the "New York credits and taxes" screen, click the Start button for "Taxes Paid to Another State" to claim the credit.

[rtang4]

Thank you for your response. I filled out the "Taxes Paid to Another State" section already, hence how I was able to eliminate the tax I owed to NYS. However, for whatever reason I still owe NYC 600 in taxes...

I'm wondering if living in NYC simply means I'll be taxed more, even though all my money has already been taxed in California.