The fact that your payment was debited from your bank account indicates that your New York State return was accepted. As for being approved, with tax returns it's a "no news is good news" situation. As long as you don't receive a letter from them, everything OK. If there was a problem with your return, you would have been notified right away. That said, the states and IRS match information with each other and with what is reported by employers, brokers, banks, etc. and taxpayer returns. It can sometimes take months or even a year or two for a discrepancy to be identified. But like I said, no news is good news.
