National Health Insurance Act Article 95

If the Insurer has paid insurance benefits to a beneficiary for any car traffic accident, the Insurer may claim against the insurer of the compulsory automobile liability insurance to recover the benefits paid.If a beneficiary has an indemnity claim against a third party arising out of an incident covered by this Insurance, the Insurer of this Insurance may, after paying insurance benefits to the beneficiary, exercise the right of subrogation in accordance with the following subparagraphs:1. Public safety incidents: The Insurer shall claim against the insurer of liability insurance, which is mandatorily required by law to be obtained from a third party. If the claim is not fully satisfied, a request may be made to the third party.2. Other serious traffic accidents, public nuisance, or food poisoning incidents: When the third party has carried his liability insurance, the Insurer shall claim against the third party’s insurer. If there is any deficit in settlement or no such insurance being carried, the Insurer shall claim against the third party for the deficit amount or the indemnity.The regulations governing the minimum compensation amount, the compensation scope, methods, and procedures of the public safety incidents, serious traffic accidents, public nuisance, or food poisoning incidents referred to in the preceding paragraph shall be prescribed by the Competent Authority.
中文原文 全民健康保險法第95條
保險對象因汽車交通事故,經本保險之保險人提供保險給付後,得向強制汽車責任保險之保險人請求償付該項給付。
保險對象發生對第三人有損害賠償請求權之保險事故,本保險之保險人於提供保險給付後,得依下列規定,代位行使損害賠償請求權:
一、公共安全事故:向第三人依法規應強制投保之責任保險保險人請求;未足額清償時,向第三人請求。
二、其他重大之交通事故、公害或食品中毒事件:第三人已投保責任保險者,向其保險人請求;未足額清償或未投保者,向第三人請求。
前項所定公共安全事故與重大交通事故、公害及食品中毒事件之最低求償金額、求償範圍、方式及程序等事項之辦法,由主管機關定之。

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