A custody case is one type of court case that can be filed to determine the rights and responsibilities of both parents towards their child. Full custody in Michigan means that one parent has been granted physical and legal custody of the child without sharing with the other parent.A person is in "custody" when they are arrested, or under other circumstances where their movement is restricted under the authority of a police officer. There are two types of custody. First is "legal" custody, which involves the ability to make decisions regarding the child's education, health and welfare. Legal custody is the responsibility of a parent to make significant decisions for the child, such as medical decisions and where the child attends school. Fill in the Case No. and Case name. Is there a chance that the courts would split the children up? Sole physical custody means that the child resides with only one parent. The other parent may or may not have parenting time or visitation rights.