La. Stat. tit. 13 § 3474
The acceptance by non-residents of the rights and privileges conferred by existing laws to operate motor vehicles on the public highways of the state of Louisiana, or the operation by a non-resident or his authorized agent, employee or person for whom he is legally responsible of a motor vehicle within the state of Louisiana, shall be deemed equivalent to an appointment by such non-resident of the secretary of state of Louisiana or his successor in office, to be his true and lawful attorney for service of process, as well as the attorney for service of process of the public liability and property damage insurer of the vehicle, if such insurer be a non-resident not authorized to do business in the state, upon whom or such insurer, may be served all lawful process in any action or proceeding against the non-resident, or such insurer, growing out of any accident or collision in which the non-resident may be involved while operating a motor vehicle in this state, or while same is operated by his authorized agent or employee. In the event of the death of such non-resident before service of process upon him, any action or proceeding growing out of such accident or collision may be instituted against the executors or administrators of such deceased non-resident, if there be such, and if not, then against his heirs or legatees, and service may be made upon them as provided in R.S. 13:3475. Process against the defendant or defendants, the non-resident, his executors or administrators, if there be such, and if not, then against his heirs or legatees, or the liability insurer of such vehicle, as the case may be, shall be of the same legal force and validity as if served upon such defendant personally.
La. R.S. § 13:3474