Each nonresident doing business in this State in his or her individual capacity, or as copartner or member of a copartnership or association required by sections 1621 and 1623 of this title to file the returns therein specified, or under any name other than his or her own, except as otherwise provided, shall appoint in writing a person having an office or place of business and residing in the town wherein the principal office of such nonresident, copartnership, or association is located, upon whom process against such nonresident may be served in an action founded upon a liability incurred in this State. Such appointment shall continue in force until revoked by a like instrument appointing another person therein residing, and having therein an office or place of business. Such instrument shall be recorded with the Secretary of State. In the event a nonresident has not appointed a process agent, and has not filed such appointment, as set forth in this section, the Secretary of State shall be such process agent. (Amended 1961, No. 217, § 1; eff. July 13, 1961; 1993, No. 221 (Adj. Sess.), § 26.)