(a) The department or a local authority may not prohibit the operation of an electric bicycle:
(1) on a highway that is used primarily by motor vehicles; or
(2) in an area in which the operation of a nonelectric bicycle is permitted, unless the area is a path that:
(A) is not open to motor vehicles; and
(B) has a natural surface tread made by clearing and grading the native soil without adding surfacing materials.
(b) The department or a local authority may:
(1) prohibit the operation of a bicycle on a sidewalk; and
(2) establish speed limits for bicycles on paths set aside for the exclusive operation of bicycles and other paths on which bicycles may be operated.
(c) The department may establish rules for the administration of this section if necessary.