Yes, it's true, because of safety issues. Some towns pass city ordinances (laws) that allow residents to drive golf carts in town, but usually they restrict it to only side streets and not any major highways.
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It is most likely true if you were driving on a public road. The citation you received from the police should tell you what florida statute number you violated or what city ordinance you violated. (If you were not within city limits, it might be a Leon County ordinance). If it's a state statute, you can go here to read state statutes - http://www.leg.state.fl.us/statutes/
If it's a city ordinance for Tallahassee, you can go here to look up Tallahassee ordinances - http://library.municode.com/index.aspx?clientId=19980. Go to same place for county ordinances - just look up Leon County.
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It also depends on who owns the roads in your neighborhood; if as my colleague stated, the road is a public road, then likely your town prohibits golf carts on public roads. If the roads a privately owned (by something like a homeowners' association), golf carts may be permitted.
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A golf cart with certain safety equipment may qualify as a "low speed vehicle" that can operate on public streets, if it is registered and insured.
There is a Florida statute that allows local governments to adopt ordinances to permit golf carts to operate on specifically designated public streets that have a speed limit of less than 35 miles an hour, with a number of limitations.
Here's a website with summary information.
You should not take this as legal advice regarding whether you can or cannot drive a golf cart in your neighborhood. If you have further questions, you might be able to call the City or County attorney's office to see if there are local ordinances that permit golf cart operation anywhere in Tallahassee or Leon County, or talk to a local attorney who can review the relevant local ordinances and the features of your golf cart.