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Visitor II

Charged NYC residence tax even though I moved

I work in NYC and lived in NYC Jan-July. I moved upstate (and commute to my NYC job), but my employer was still charging me NYC residence tax from Aug-Dec (they claim they couldn't change it because of some issue with our payroll system). I've already filed my 2017 taxes and received a New York State refund of ~$300. 

 

I'm assuming that, even though my employer withheld too much for NYC residence taxes (totaling ~$1,500), it eventually evened itself out when I filed my NY State return. Had they not withheld the incorrect amount, I likely would have owed NYS rather than getting a refund. Is this accurate?