Your post makes no sense. Serve what? (And the police do not serve anything).
A certificate of service is a document from a person who has already served something proving or swearing that he did.
Your question makes it sound like you are about to do something without a lawyer where you desperately need to see a lawyer.
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If you plan on serving your wife with divorce papers. You will need to go the Superior Court in the county your wife lives in, fill out the necessary paperwork (Complaint for Divorce, Domestic Information Form, Summons, and Sheriff's Entry). Once the court costs are paid and the Complaint has been filed, the Sheriff's Department with serve your Wife. You do not need a Certificate of Service.
You should speak with an attorney first.
I would agree with the previous answer insofar as it sounds like you probably need to retain an attorney. Civil law, specifically family law, is a difficult area to navigate even for attorneys. The answer to your questions depends specifically on where your case is procedurally. I would recommend hiring an attorney because once a case is complete, the results are permanent and modifying a court order can be difficult.
The above is general information and not intended to be legal advice.
When you file in your Complaint and any ancillary documents, you will have the opportunity to have the documents served by the sheriff. This usually costs about $50.00 or so, depending on the county. The clerk will forward the documents to the sheriff if you choose to have them served in that manner--so you do not personally need to send anything to the sheriff.
If you are initially placing the "papers" in the other party's hands, you are "serving" the opposing party. You may "serve" that person in one of four ways. First, you may ask them to sign a form called an "acknowledgment of service" in the presence of a notary. You must file this acknowledgment with the clerk of the court to prove the service occurred. Second, the opposing party may allow the opposing party's attorney to sign the acknowledgment. It would then need to be filed with the clerk, same way. Third, you may have the sheriff in the county where the opposing party resides serve the papers on the person or upon an adult who lives at the person's residence. You may also have a private process server do this (as long as the process server has been approved by the judge to serve the papers). The sheriff will then complete a form which is filed with the clerk to prove that the service occurred. Finally, if you have no idea where the other party is, you may go through a process to serve the person through publication in the media. This is complicated, and the details go beyond the scope of your question.
Why do this? Because the law says you have to do this in order for the Court to have personal jurisdiction over the defendant (the person you served). Without doing this in one of these four ways, the Court will not hear your case.
After initial service has occurred, the term "certificate of service" means that you are certifying to the court how you send subsequent pleadings and documents to the opposing party. In each case, you are sending a form to the court which says what you sent to the other party and how (for example, a subpoena for documents, by hand delivery or by regular mail).
I hope this helps you..
If you are having your wife served by a Sheriff, then there is no need for you to file a Certificate of Service. Once the Sheriff actually perfects service upon your wife, he/she will complete a Sheriff's Entry of Service and file it in the Superior Court's Clerk's office.
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