In general a special-purpose district is a government district like a municipality, county, etc. (general-purpose districts), but for a special purpose only. A good example of a special-purpose district would be the school-district. Special districts are sometimes created to deal with fire protection, sewage, or to manage water resources. These districts are usually much more flexible than the more geographically determined municipalities and townships.
There are two types of special-purpose districts. Some are independent, in that they are allowed to tax, and others are dependent in that they are not allowed to tax.
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