Under Indiana law, the local school district can establish dress codes. Here is what the law says:
Adoption of discipline rules; publicity requirement; discipline policy regulations and guidelines; delegation of authority; rulemaking powers of governing body
Sec. 12. (a) Except as provided under IC 20-33-8-16, the governing body of a school corporation must do the following:
(1) Establish written discipline rules, which must include a graduated system of discipline and may include:
(A) appropriate dress codes; and
(B) if applicable, an agreement for court assisted resolution of school suspension and expulsion cases; for the school corporation. (2)Give general publicity to the discipline rules within a school where the discipline rules apply by actions such as: (A) making a copy of the discipline rules available to students and students' parents; or (B) delivering a copy of the discipline rules to students or the parents of students. This publicity requirement may not be construed technically and is satisfied if the school corporation makes a good faith effort to disseminate to students or parents generally the text or substance of a discipline rule. (b) The: (1) superintendent of a school corporation; and (2) principals of each school in a school corporation; may adopt regulations establishing lines of responsibility and related guidelines in compliance with the discipline policies of the governing body. (c) The governing body of a school corporation may delegate:
(2) disciplinary; and
(3) other authority; as reasonably necessary to carry out the school purposes of the school corporation.
(a) does not apply to rules or directions concerning the following:
(1) Movement of students.
(2) Movement or parking of vehicles.
(3) Day to day instructions concerning the operation of a classroom or teaching station.
(4) Time for commencement of school.
(5) Other standards or regulations relating to the manner in which an educational function must be administered. However, this subsection does not prohibit the governing body from regulating the areas listed in this subsection. As added by P.L.1-2005, SEC.17. Amended by P.L.242-2005, SEC.22; P.L.66-2009, SEC.3.
If you give me more time, I will see if there is case law from the Indiana courts that limit the dress code making authority.