The banking (Citicard) in the New York market goes to India. I'm not sure about the credit card, but I would not be surprised.
Quite recently I called regarding a checking plus line (10 AM EST) and they told me to call again the next day because the person who could help was not around. (Amazing!)
The lady had an indian accent. When I asked her if she was in India she said "No.". (Liar!)
I found it baffling that Citibank would ask me to call the next day when I was calling during business hours, so I called my banker and found a back-door number to the US call center.