Legal provisions for mandatory referendums at national level

Constitution of Japan (Came into effect May 3, 1947; not amended since)

Article 79 (1) The Supreme Court shall consist of a Chief Judge and such number of judges as maybe determined by law; all such judges excepting the Chief Judge shall be appointed by the Cabinet.
(2) The appointment of the judges of the Supreme Court shall be reviewed by the people at the first general election of members of the House of Representatives following their appointment, and shall be reviewed again at the first general election of members of the House of Representatives after a lapse of ten (10) years, and in the same manner thereafter.

(3) In cases mentioned in the foregoing paragraph, when the majority of the voters favours the dismissal of a judge, he shall be dismissed.

(4) Matters pertaining to review shall be prescribed by law.

(5) The judges of the Supreme Court shall be retired upon the attainment of the age as fixed bylaw.
(6) All such judges shall receive, at regular stated intervals, adequate compensation which shall not be decreased during their terms of office.

Article 96

(1)  Amendments to this Constitution shall be initiated by the Diet, through a concurring vote of two-thirds or more of all the members of each House and shall thereupon be submitted to the people for ratification, which shall require the affirmative vote of a majority of all votes cast thereon, at a special referendum or at such election as the Diet shall specify.

(2) Amendments when so ratified shall immediately be promulgated by the Emperor in the name of the people, as an integral part of this Constitution.

The first review of a judge (at the first general election after his or her appointment) can be seen as an election issue, but subsequent reviews, held at ten year intervals, can be reasonably interpreted as referenda.