What law says Jews could not put any criminal to death?

The law that states Jews could not put any criminal to death is derived from the Roman legal framework imposed during the time of the Second Temple. Specifically, after the destruction of the Temple in 70 CE, the Sanhedrin, the Jewish court, lost its authority to impose capital punishment, which was a significant aspect of Jewish law. This situation was further codified in the Talmud, where it is discussed that the Romans restricted Jewish legal authority, thus preventing Jews from carrying out death sentences.