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Transcutaneous injection laryngoplasty (TIL) is a commonly used method to treat vocal fold paresis, where the affected vocal folds are augmented through injection. Determining the injection site and route is a major step during the preprocedural planning of TIL. In this communication, we propose and investigate an automatic method for needle route computation in preoperative neck CT. Recently, deep reinforcement learning (RL) agents showed noteworthy results for localizing the vocal folds. In this work, we focus on finding the optimal needle trajectory from the neck skin to the vocal folds localized by such RL agents. Identifying critical structures and constraints in the medical routine, we propose a minimal cost-based search to find the optimal path. Furthermore, we evaluate the proposed method with neck CT volumes from 136 patients, where it is shown that our computed needle paths have high accuracy. [ABSTRACT FROM AUTHOR]