I checked Municode for Ludington and this is all that came up specific to firearms for them.
Sec. 34-100. - Firearms and weapons.
(a) The following words, terms and phrases, when used in this section, shall have the meanings ascribed to them in this subsection, except where the context clearly indicates a different meaning:
Dangerous weapon means any instrument or device which is either designed to cause physical injury or death or which is used or intended to be used in a manner likely to cause serious physical injury or death.
Firearm means any instrument or device included within the provisions of section 222 of the Michigan Penal Code (MCL 750.222, MSA 28.419) or Public Act No. 189 of 1959 (MCL 8.3t, MSA 2.212(20)).
(b) No person shall shoot, discharge or otherwise use a firearm, crossbow, slingshot or other dangerous weapon in any street, avenue, alley, parking lot, public place or on private property within the city or shoot or discharge any bow and arrow in a manner which carelessly or recklessly endangers any person or property.
(c) This section shall not apply to the following:
(1) Any peace officer of a duly authorized police or correctional agency; members of the United States armed forces, reserves or national guard; or members of any other duly authorized governmental or military organization of the government of the United States or of the state, when in furtherance of the purpose of such agencies or organizations.
(2) Any person who is properly licensed or who has a valid permit when that person is acting within the lawful purpose or scope of the license or permit.
(3) Any person on the premises of a duly authorized or licensed business or profit or nonprofit organization lawfully engaged in the selling, exchanging or collecting of weapons, if in furtherance of that purpose, or when lawfully on the premises of a duly authorized or licensed business or profit or nonprofit organization, the purpose of which is to provide targets for practice or for sport, if in furtherance of that purpose.
(d) Nothing in this section shall be construed to allow what the state law specifically prohibits.
No specific mention of OC but, as Bronson stated, it would be preempted at the state level even if there was a specific ordinance.