The Coast Guard Act Article 9

To check smuggling, crack down illicit entry or exit, and investigate any crime, the personnel of the Coast Guard may, in an emergency, take the liberty of investigating a crime committed by a suspect and searching/collecting evidence outside the precinct, and inform the related authority of this right away.
中文原文 海岸巡防法第9條
海巡機關人員執行查緝走私、非法入出國及其他犯罪調查職務,遇有急迫情形時,得於管轄區域外,逕行調查犯罪嫌疑人之犯罪情形及蒐集證據,並應立即知會有關機關。

English translation for reference only; the Chinese text prevails. Not legal advice.