Concussion Treatment and Care Tools Act of 2013 or ConTACT Act of 2013 - Amends the Public Health Service Act to direct the Secretary of Health and Human Services (HHS) to establish guidelines for states on the implementation of best practices for diagnosis, treatment, and management of mild traumatic brain injuries (MTBIs) in school-aged children, including best practices relating to student athletes returning to play after an MTBI.

Requires the Pediatric MTBI Guideline Expert Panel of the Centers for Disease Control and Prevention (CDC) to issue a final report on such best practices by March 15, 2015.

Authorizes the Secretary to make grants to states for: (1) adopting, disseminating, and ensuring school implementation of the guidelines; and (2) ensuring elementary and secondary schools implement computerized preseason baseline and post-injury neuropsychological testing for student athletes.

Directs the Secretary to require states receiving grants to utilize, to the extent practicable, applicable expertise and services offered by local chapters of national brain injury organizations.