No, according to IRS Publication 575, page 34, you are a qualified public safety employee if you provided police protection, firefighting services, or emergency medical services for a state or municipality.
You can find the link to that publication below:
I believe a prosecutor does qualify. IRS Pub 575 defines a PSO as including a "law enforcement officer." The Public Safety Officers’ Benefits Act (the law that established the credit), as well as the regs that implement it, include prosecutors in the definition of law enforcement officer. For example, in the Act (42 USC 3769b), the term law enforcement officer means an individual “involved in crime . . . control or reduction, or enforcement of the criminal laws,” and includes "judicial officers.” And in 28 CFR 32.3, “involvement” in crime control or enforcement includes those with authority to “prosecute"; and "law enforcement" includes “prosecution or adjudication.”