The state highway patrol shall have the same authority as is conferred upon it by section 5503.02 of the Revised Code with respect to the enforcement of state laws on other roads and highways and on other state properties, to enforce on all turnpike projects the laws of the state and the bylaws, rules, and regulations of the Ohio turnpike and infrastructure commission. The patrol, the superintendent of the patrol, and all state highway patrol troopers shall have the same authority to make arrests on all turnpike projects for violations of state laws and of bylaws, rules, and regulations of the Ohio turnpike and infrastructure commission as is conferred upon them by section 5503.02 of the Revised Code to make arrests on, and in connection with offenses committed on, other roads and highways and on other state properties.