I am only familiar with seeing alimony taxed when you add it to income on Federal and State tax forms. Usually medicare is taken out of gross earnings by employer, and local (as in city or municipal) taxes often don't involve a filing.
I suspect you may be over analyzing there a bit. If she declares it as income on all forms filed, I would find it doubtful she could be found in willful contempt for not paying medicare or city taxes, and I don't see a city coming after her for the local taxes. But perhaps someone on here knows more about this than I do -- my knowledge of city taxes is limited to a couple of places, and no tax forms had to be sent in where I lived.
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