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The local income tax rate can be found at the state website. It is a flat rate against your entire taxable income that can change every year.
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The "piggyback tax" existed in Maryland for many years, when the county tax was expressed as a percentage of the state tax liability. With the income tax changes passed by the state legislature in 1998, the rates for all counties and the City of Baltimore were "decoupled" from the state rate. Each county and the City of Baltimore has its own tax rate as determined by the state legislature unless changed by the local legislative body.