A complainant can decide not to pursue a Title IX investigation under the Title IX Final Rule. If a complaint is received by the school for example, if it gets to the Title IX coordinator and if the complainant is not looking to pursue the matter, not looking to sign the formal complaint, the complainant can choose not to do so. That being said, the school will take into account the complainants wishes. This has not changed under the Title IX Final Rule.
Also what has not changed is the fact that if it's clearly not unreasonable to the circumstances, the Title IX coordinator, him or herself can sign a formal complaint and the school can pursue the investigation. Although a complainant can decide to not pursue a case, the school itself can take it upon itself to do so. Again, if it's clearly not unreasonable in light of the circumstances. If you're facing a Title IX concern or a Title IX sexual misconduct case, having an experienced attorney advisor can help you navigate the process and can help you work towards trying to ensure a fair process and favorable outcome. They should be involved from as early as possible in the process.