It depends. Without seeing your return (and most likely doing the actual calculations) it’s not possible to tell you whether you are better off filing together or separately for state taxes.
Both states will calculate your tax as if all income were earned in that state if you file jointly, so you’ll effectively be paying a higher tax rate by filing together. However, you may have deductions or credits that would make joint filing more beneficial.
You can also claim a credit on both the NY and DC return for tax paid to the other state you are would be filing two resident returns.
D.C. also has a statutory resident rule, meaning any individual who maintains a place of abode within the District for an aggregate of 183 days or more during the taxable year, whether or not such individual is domiciled in the District. As a married couple, the NY resident may potentially be considered a D.C. resident.
To prepare a joint federal and separate state returns see: How do I prepare a joint federal return and separate state returns?
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