The speed limits and location of traffic control signs on private roads subjected to the Uniform Act Regulating Traffic pursuant to § 56-5-6310 shall be established as follows:

(a) The owner of the private roads or both owners, or a majority of the owners, as the case may be, shall submit proposed speed limits and proposed locations for traffic control signs to the sheriff of the county in which the roads are situate and shall obtain the sheriff’s written approval of such speed limits and traffic control signs. Such approval shall be filed with the clerk of court or register of deeds and the affected roads then posted by signs identical or similar to those used on public roads.

(b) After filing with the clerk or register such speed limits and traffic control signs shall become effective as soon as they are posted on signs and thereafter may be enforced by the State Highway Patrol, officers of the sheriff’s department and state constables appointed by the Governor, in addition to any other persons having authority to take out warrants or make arrests.