It depends. NY does not tax income you earned in Maryland after moving to Maryland (unless you are telecommuting with your old NY job. If this is the case, please comment and I'll give an additional explanation). However, NY will factor in all of your income to determine your NY tax. What NY does is determine how much tax you would pay on all of your income, and then prorate the amount to the percentage of income earned in New York.
For instance, if you earned 30K in New York and 20K in Maryland after moving, then NY will figure out your tax on 50K. Let's say that amount is 2,000. Your NY tax will be 1,200, which is 60% of the amount, since 60% of your income was earned in NY.
The reason behind this is two-fold. First, this allows NY to correctly apply any deductions and credits to the same ratio as your tax. However, it also gives them an opportunity to have you (potentially) in a different tax bracket, which can raise your taxes on your NY income, even though your Maryland income is not taxed in NY.
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