Why am I owing over $200 in ny taxes, when I only worked in new york for a month and did not live there.

I am assuming you are asking why you owe $200 to NY?  

As a non-resident, NY will still tax your income.  So if you are single and have NY taxable income of $5,000 for that one month, then you would have a tax liability to NY for $200.  If you did not have any taxes withheld to pay that liability, then you would now have to pay when you file your Non Resident Return.

Depending on which state you live in, you may be able to take a credit for taxes paid to another state on your return which may lower your taxes due to your home state.  However, if your home state has a lower tax rate, then you will not receive the full $200 credit, but the income that was taxed by NY will not be taxed again by your home state. 

Multiple States

File Non Resident State Return