Prosecutors Need to Prosecute Act of 2023 This bill requires certain state and local prosecutors to report data on criminal referrals and outcomes of cases involving murder or non-negligent manslaughter, forcible rape, robbery, aggravated assault, burglary, larceny, motor vehicle theft, arson, or any offense involving the illegal use or possession of a firearm. The reporting requirement applies to state and local prosecutors in a jurisdiction that has 360,000 or more persons and receives funding under the Edward Byrne Memorial Justice Assistance Grant (JAG) program. The report must contain data on cases referred for prosecution, cases the prosecutor declined to prosecute or refer for diversion, cases for which the prosecutor declined to reach a plea agreement, cases that resulted in a plea agreement or referral for diversion, and offenses the prosecutor dids not prosecute due to an internal policy. If a state or local prosecutor complies with these requirements, the bill requires (1) the Department of Justice to give priority in disbursing Byrne JAG program funds to the local government served by the prosecutor, and (2) the local government to ensure that the prosecutor receives a portion of the funds. Additionally, the bill prohibits states and local governments from receiving funds under the Byrne JAG program if they have in effect a policy that prohibits the use of cash bail for a defendant in a case involving the illegal use or illegal possession of a firearm.