Victims do have specific rights in some states (for instance, since 1994, the Ohio Constitution has included the following provision), but the prosecutor has the last word as to whether or not to go forward with a case:
§1.10a. Rights of victims of crime.
Victims of criminal offenses shall be accorded fairness, dignity, and respect in the criminal justice process, and, as the general assembly shall define and provide by law, shall be accorded rights to reasonable and appropriate notice, information, access, and protection and to a meaningful role in the criminal justice process. This section does not confer upon any person a right to appeal or modify any decision in a criminal proceeding, does not abridge any other right guaranteed by the Constitution of the United States or this constitution, and does not create any cause of action for compensation or damages against the state, any political subdivision of the state, any officer, employee, or agent of the state or of any political subdivision, or any officer of the court.