Each town in Indiana can add some restrictions if the city council votes in favor of the additions. Most police officers do not bother with golf carts as they do not want to go to traffic court over them except in your case somebody complained.
Keep in mind that many highways do have rules that do not allow slow vehicles such as golf carts to travel on them. A person would just have to check this out in their area.
Here in Bicknell I was talking to a police officer who was driving around in a golf cart handing out papers as he is trying to be a Bicknell councilman but even in this case I don’t believe that the Bicknell City Council ever actually passed an ordinance concerning the city requirements for golf carts.
In your case it appears that you have a neighbor who is either jealous of you or doesn’t like you for some reason.
Code:
DIGEST OF HB1483 (Updated April 27, 2009 11:53 am - DI 84)

Off-road vehicles, farm wagons, and golf carts. Defines "farm wagon" as including three, four, and six wheeled motor vehicles with a folding hitch that is used for certain purposes. Prohibits a certain type of farm wagon from operation on an interstate highway, or a state highway, except under specific circumstances. Authorizes an individual at least 15 years of age to operate a motorized farm wagon on a highway. Prohibits the use of a motorized farm wagon operated on a highway to tow another vehicle. Prohibits an

individual from operating a golf cart on a highway, except when a city or town has adopted an ordinance (ordinance) authorizing the use of golf carts on the city's or town's highways. Specifies that an ordinance: (1) may require that a golf cart display a slow moving vehicle sign or a red or amber flashing lamp; and (2) must require an individual operating a golf cart in the city or the town to hold a driver's license. Requires financial responsibility for golf carts operated pursuant to an ordinance. Requires a person removing a wrecked or damaged golf cart from a highway to remove any glass or other foreign material dropped upon the highway from the golf cart. Makes conforming amendments.
Current Status:
Law Enacted
IC 9-21-1-3.3
Ordinances regarding use of golf carts on highway
Sec. 3.3. (a) A city or a town may adopt by ordinance traffic regulations concerning the use of golf carts on a highway under the jurisdiction of the city or the town. An ordinance adopted under this subsection may not:
(1) conflict with or duplicate another state law; or
(2) conflict with a driver's licensing requirement of another.
Contact your city hall and request their ordinance regarding golf cart operation instead of simply taking the officers statement as to whether or not your cart is legal or not.
Hope this helps
John R. Stanczak