If the state does not prohibited it, a city can do just that. The New York City has a city income tax I believe.
NYC or NY residents please verify.
Every county in Maryland and Baltimore city has an income tax in addition to the state income tax.
If that were so, every major Democrat-run city in the country would have a municipal income tax by now.
You say that New York City has one, but you're not sure. I've never heard of a municipal income tax anywhere. Anyone else ever hear of this?
NYC does have an income tax; those NJ people bemoaning the horrible train situation pay it as well (for working in NYC).