certificate of residence
An official document issued by a municipal office that certifies a person's registered address in Japan. Often required for administrative procedures.
A certificate of residence is required to open a bank account.
I had a certificate of residence issued at the city hall.
住民票 is the resident record itself, while 居住証明書 is a certificate that proves residence based on that record. 住民票 is more commonly used in daily conversation.
Compound of 居住 (residence) + 証明書 (certificate). A straightforward modern administrative term.