Genin no Yukue wo Oikakete

In a bid to save the broadcasting club from disbandment, protagonist Yuto Shimoda is tasked with reading "Rashomon" for the upcoming reading contest.
But he feels somehow detached from the assignment.
That is, until he encounters a girl in the broadcast room at school whose acting prowess eerily evokes the old woman from "Rashomon."

Source: MangaPlus