The determination of how to handle an alleged defamatory (libel (written) or slander (verbal)) statement or act involves a number of factors. First, you need to be aware of the statute of limitations in your jurisdiction. You will need to file any legal action prior to the expiration of the statute of limitations.
Second, what exactly were the false statements? Not all false statements are defamatory. If the false statements fall into certain categories (such as accusing an individual of a criminal act), the statements may be defamatory per se for which damages need not be proven. In such a case, damages may be presumed. If a statement is not defamatory per se, it will be considered defamatory per quod. For such statements, damages will need to be proven. In some jurisdictions, proving actual damages will be difficult unless clear economic damages or some other substantive act has occurred causing specific harm.
Third, did anyone actually believe the false statement? Often, a false statement will be made about an individual that no one believes. In such a case, it would be difficult to succeed on a defamation claim.
Fourth, you cannot likely succeed in preventing someone from communicating a statement in the future. Rather, the remedies, if any, will arise subsequent to an actionable statement being made. That being said, if the conduct rises to the level of harassment or some other claim, exceptions may be possible in this regard.
Fifth, would you benefit from litigation? Are you seeking damages? If so, how much? Does the potential defendant have the ability to pay for the damages you seek? Will the litigation cause more harm than good? How will the individual(s) react?
There exist numerous factors, questions, and issues to consider. Sometimes, litigation is necessary. Sometimes, it may be better to ignore the matter. Still, other times, a resolution can be obtained with the use of an attorney that does not involve litigation.
I would recommend speaking with an attorney who can discuss all of the options and obtain more details on the facts involved.
Slander is an untruthful spoken statement about a person that harms the person's reputation or standing in the community. As but one example, a damaging untruthful spoken statement that you are a criminal might be defamation "per se". Contact a local lawyer - many may give you a free consultation for an hour - to discuss your specifics. Far too many variables exist in the short post you wrote for any further observation by me.
You need a lawyer. Check with a lawyer in your locale to discuss more of the details.
You might find my Legal Guide helpful "How to Choose A Lawyer For You"
You might find my Legal Guide helpful " What Do I Tell My Lawyer"
Good luck to you.
NOTE: This answer is made available by the out-of-state lawyer for educational purposes only. By using or participating in this site you understand that there is no attorney client privilege between you and the attorney responding. This site should not be used as a substitute for competent legal advice from a licensed professional attorney that practices in the subject practice discipline and with whom you have an attorney client relationship along with all the privileges that relationship provides. The law changes frequently and varies from jurisdiction to jurisdiction. The information and materials provided are general in nature, and may not apply to a specific factual or legal circumstance described in the question.
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