Accidents involving death or personal injuries.
(a) The driver of any motor vehicle involved in an accident resulting in injury to or the death of any person, or in damage to a motor vehicle or other vehicle which is driven or attended by any person, shall immediately stop such vehicle at the scene of such accident or as close thereto as possible and shall then forthwith return to and in every event shall remain at the scene of the accident until he has fulfilled the requirements of Section 32-10-3. Every such stop shall be made without obstructing traffic more than is necessary.
(b) The director shall revoke the driver's license of a person convicted under this section.
The title might say death or personal injuries but there's an "or" in the text that results in the following:
"The driver of any motor vehicle involved in an accident resulting in... damage to a motor vehicle or other vehicle which is driven or attended by any person"
Since your vehicle was apparently damaged and needed a tow truck, and you are, of course "any person", I think that statute obligated you to remain at the scene.
What I don't understand is why you left in the first place. You apparently left your car behind for the tow and the trooper showed up while the car was being hooked up? Where did you go and who took you there? Was it your intention to lie low till the alcohol wore off? Doesn't make sense not to stay with the car till the tow truck shows up and gets it.