Who prosecutes election-related criminal offences?

The National Prosecuting Authority Act (2014) vests the responsibility of instituting criminal proceedings in the Prosecutor General in accordance with the 2013 Constitution, 

Constitution of Zimbabwe (2013)

https://www.constituteproject.org/constitution/Zimbabwe_2013.pdf

Art 114(4): The functions of the Attorney-General are.

            a. to act as the principal legal adviser to the Government;

            b. to represent the Government in civil and constitutional proceedings;

            c. to draft legislation on behalf of the Government;

            d. to promote, protect and uphold the rule of law and to defend the public interest; and

            e. to exercise any other functions that may be assigned to the Attorney-General by an Act of Parliament;

Art 258: There is a National Prosecuting Authority which is responsible for instituting and undertaking criminal prosecutions on behalf of the State and discharging any functions that are necessary or incidental to such prosecutions.

Art 259(1): There is a Prosecutor-General who is the head of the National Prosecuting Authority