At a K-12 school, cross-examination would work either at a live hearing, where the cross-examination would take place directly orally and in real time at the live hearing. It can also take place prior to the hearing, say, at schools that either use the hearing process or make a determination regarding responsibility without having a hearing. With or without a hearing, after the investigative report is provided to the parties and before a determination regarding responsibility is made, the decision-makers must allow the parties to present written relevant questions to any party or witness. They must then, in response, provide the answers to the parties that had asked said questions, and then they must also allow limited follow-up regarding any further questions to the party.
Cross-examination and further questioning can and would take place at a K-12 school both with and without a hearing. Having an experienced attorney advisor will be your best ally in helping to understand and navigate the Title IX process. They should be involved from as early as possible in a Title IX case.