I would agree that given the circumstances, the police way overreacted. At this point, the case will go to the prosecutor's office for review who will make a determination whether to charge you or not. The prosecutor has to be able to prove neglect beyond a reasonable doubt. Here is the statute:
§ 11-9-5 Cruelty to or neglect of child. –
(a) Every person having the custody or control of any child under the age of eighteen (18) years who shall abandon that child, or who shall treat the child with gross or habitual cruelty, or who shall wrongfully cause or permit that child to be an habitual sufferer for want of food, clothing, proper care, or oversight, or who shall use or permit the use of that child for any wanton, cruel, or improper purpose, or who shall compel, cause, or permit that child to do any wanton or wrongful act, or who shall cause or permit the home of that child to be the resort of lewd, drunken, wanton, or dissolute persons, or who by reason of neglect, cruelty, drunkenness, or depravity, shall render the home of that child a place in which it is unfit for that child to live, or who shall neglect or refuse to pay the reasonable charges for the support of that child, whenever the child shall be placed by him or her in the custody of, or be assigned by any court to, any individual, association, or corporation, shall be guilty of a felony and shall for every such offense be imprisoned for not less than one year nor more than three (3) years, or be fined not exceeding one thousand dollars ($1,000), or both, and the child may be proceeded against as a neglected child under the provisions of chapter 1 of title 14.
(b) In addition to any penalty provided in this section, any person convicted or placed on probation for this offense may be required to receive psychosociological counseling in child growth, care and development as a part of that sentence or probation. For purposes of this section, and in accordance with § 40-11-15, a parent or guardian practicing his or her religious beliefs which differ from general community standards who does not provide specified medical treatment for a child shall not, for that reason alone, be considered an abusive or negligent parent or guardian; provided, the provisions of this section shall not: (1) exempt a parent or guardian from having committed the offense of cruelty or neglect if the child is harmed under the provisions of (a) above; (2) exempt the department from the provisions of § 40-11-5; or (3) prohibit the department from filing a petition, pursuant to the provisions of § 40-11-15, for medical services for a child, where his or her health requires it.
Ultimately, the state decides whether to press charges. Whether they can prove that you "abandoned" the child is the question - leaving the child alone for a few minutes arguably isn't abandonment, even though yes, anything could have happened to the child at that time, which is likely what caused the police to arrest you. The fact that the child wasn't injured and that child services also isn't taking action is helpful.