Usually the way criminal charges work is that the arresting or investigating agency will turn in all relevant documents to the District Attorney and then the DA will decide if there is enough evidence to support a trial or if the case should be dismissed. From there the DA will present the case in front of the Grand Jury (in some states), this is not a trial and the defendant usually is not present. In this process there is no 'one person' responsible for charging an alleged criminal.
against..... the arrestee (known as the defendant).
The State brings an action against a defendant.
who brings the case to court
Charges are typically brought up by a prosecutor on behalf of the government in a criminal case. In civil cases, charges are usually initiated by the plaintiff or their attorney.
prosecuting attorney
Plaintiff usually refers to when someone is bring a civil lawsuit against a defendant (i.e. when money is involved) whereas prosecutor involves the government filing charges against a defendant (usually involves a criminal charge).
The House of Representatives is the one that can impeach the president or other federal officials.
When a person commits perjury in any court, including family court, the DA will being charges. In some cases, the judge will bring the charges against the person and sentence the person to jail.
In the impeachment process, the House of Representatives brings charges with a 2/3 majority vote. It is then up to the Senate to confirm the charges.
House of representatives
In the criminal system, it is the government that brings a case against a defendant, and in civil court, citizens can bring lawsuits against one another. ... For instance, prison is a possibility in certain criminal cases, whereas civil cases do not punish the accused with incarceration.
Question isn't entirely clear. If party "A" brings charges against party "B" - party "B" can bring charges against party "A" if they can convince the police or the prosecutor that an offense actually took place and they are not just doing it as retaliation.