The following documents are required to prepare for either renting or purchasing a car:

Rental contract required documents

Required purchase contract documents

Residence card

Seal registration certificate

Residence record (confirming you live in the area)

Registered stamp (hanko / inkan)

In Japanese:

賃貸契約必要書類

・免許証

購入必要契約書

・住民票

・印鑑証明

・在留カード