The House of the Baglioni by K.C. Tunstall — a scholarly but readable account of the rise and fall of the Baglioni family, the ruthless noble clan who dominated Perugia through the 15th and early 16th centuries. Their internecine murders, coups, and eventual destruction by the papacy are the background story to everything built in Perugia during its greatest artistic period.
Umbria: The Heart of Italy by Paul Hofmann — a journalist's portrait of the region written in the 1970s, covering Perugia, Assisi, and the smaller hill towns with a good eye for the texture of daily life. Dated in places but still evocative.
The Agony and the Ecstasy by Irving Stone — a biographical novel about Michelangelo rather than Perugia specifically, but the Umbrian chapters (Michelangelo trained briefly in Perugia) give a good sense of the competitive, violent world of Renaissance Italian city-states in which Perugia was a significant player.