If you're involved in a small-claims case, state law and local court rules will set out the procedures for requesting a dismissal, either as a plaintiff or defendant. In most cases, you'll use specific legal documents, either an original pleading or a specific form created and used by the court. Standard business or personal letters don't function as pleadings or requests in court.
Dismissal Conditions
Requesting a dismissal means asking the court to terminate the case, with no decision going to either plaintiff or defendant. You must have grounds to request dismissal of your own claims or those of your opponent. A defendant can have a case dismissed if the plaintiff has misspelled his name, for example, or has neglected to sue the proper corporate entity. A plaintiff can move for voluntary dismissal if he's simply decided to drop the case, or has been reimbursed by the defendant for any damages.
A dismissal "with prejudice" means the same court will not consider the same matter in the future. "Without prejudice" means a plaintiff may bring the case up again, after making any needed corrections to his claim.
Dismissal Forms and Pleadings
Either party can file a motion to dismiss by creating an original document that uses the proper format for court pleadings. Alternatively, a small-claims court may provide a form, much like the original Notice of Claim form, which the movant fills out with required information and provides to the court and the other party. Sending a business letter to a clerk or judge in regards to a pending case generally is ineffective and ill-advised -- such "ex parte" communications from one party or the other to the court are a serious breach of legal etiquette.
Letters to the Court
Small-claims courts are generally less strict about their own procedures and rules. In the interest of expediting cases on a crowded docket, a small-claims judge may accept a notarized letter signed by both parties setting out grounds for dismissal of the claim, and cancel a scheduled hearing.
However, the judge also may require the presence of both parties at a hearing to gather relevant testimony and evidence, and then render a decision to either dismiss the case or allow it to go forward for a decision by the court. If both parties fail to appear, the court may dismiss the case but also assess costs and penalties against the absent parties.