§48-10-702. Proof required when action is not pending for divorce, custody, legal separation, annulment or establishment of paternity.
(a) If a petition is filed pursuant to section 10-402 when the parent through whom the grandparent is related to the grandchild does not: (1) Have custody of the child; (2) share custody of the child; or (3) exercise visitation privileges with the child that would allow participation in the visitation by the grandparent if the parent so chose, the grandparent shall be granted visitation if a preponderance of the evidence shows that visitation is in the best interest of the child.

(b) If a petition is filed pursuant to section 10-402, there is a presumption that visitation privileges need not be extended to the grandparent if the parent through whom the grandparent is related to the grandchild has custody of the child, shares custody of the child, or exercises visitation privileges with the child that would allow participation in the visitation by the grandparent if the parent so chose. This presumption may be rebutted by clear and convincing evidence that an award of grandparent visitation is in the best interest of the child.