If the suit was filed in Florida, the Florida Rules of Civil Procedure govern.
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If the subject matter does not involve a business transaction, then the law of how a summons is to be served is governed by F.S. Section 48.194. You are right to hire a certified process server in Atlanta and he is also right that you must use FL law of service on non-residents. However, this still means you must serve these defendants according an authorized officer in the state of Georgia. If your suit involves a business transaction in this state, follow F.S Section 48.181. If you do not have luck with this process server in Atlanta, try a different authorized process server. Good luck.
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If your question is how to serve process on persons living outside the state of Florida, then Ms. Morghem has pointed you in the right direction. Subject to the exceptions provided in the statute identified in her response, section 48.194(1) provides, in pertinent part: “service of process on persons outside of this state shall be made in the same manner as service within this state by any officer authorized to serve process in the state where the person is served.” Problems can and do arise when a process server serves process in a manner consistent with the law of the state in which service is made but inconsistent with the laws of Florida. For example, some states permit service of process on Sundays and Sundays are often a good day to find a person at home. However, section 48.20, Florida Statutes provides that service of process on a Sunday is void. Whether the facts support service of process through section 48.181, Florida Statutes, as Ms. Morghem suggests as a possible alternative, involves an analysis of your cause of action and the business being conducted in Florida. Clearly, a civil litigation attorney will afford you the best chance for obtaining valid service of process in your case and will be able to address on your behalf any challenge to service of process or jurisdiction that may come your way.