Yes and no. State laws make no distinction, but many cities and towns add restrictions, usually to protect pedestrians. I compared the laws of four area communities: Chicago, Elkhart, Mishawaka, and South Bend.
South Bend has the most straight forward ordinance: “No person shall ride a bicycle upon a sidewalk within any business district.” Interestingly, it fails to define a ‘business district’. At least I couldn’t find a definition.
Chicago has the same ‘business district’ restriction as South Bend, but adds some complexity. Adults (and children 12 years and older) can’t ride on any sidewalk anywhere. There are a few exceptions, and they will be so indicated with bicycle route signage.
Elkhart is pretty straight forward. Bikes are permitted on sidewalks except in a clearly defined area of downtown. See the above map. Interestingly, Elkhart just redefined the area: until last month, the restricted area was about three times the size of the current district.
Mishawaka has the most restrictive ordinance: “No person shall ride a bicycle on the sidewalk or on any public right-of-way within the downtown business district, except in such places as are marked as bicycle paths.” The ordinance goes on to define the downtown business district. The definition is 403 words long and reads like a legal description.
In the opinion of most experienced cyclists, children belong on the sidewalk, but adults are better off in the roadway in most cases. The League of American Bicyclists points out that riding on the sidewalk is a significant cause of crashes: at every driveway and intersection bikers can surprise motorists who are simply not looking out for them. For sidewalk riders, the LAB recommends riding at walking speed and stopping or yielding at every intersection.