Who can initiate an optional referendum at the national level?

Constitutionof Uganda(1995)

http://www.opm.go.ug/assets/media/resources/6/Constitution.pdf

Article 74. Change of political systems by referenda or elections.

(1) A referendum shall be held for thepurpose of changing the political system-

  (a) if requested by a resolution supported by more than half of allmembers of Parliament; or

  (b) if requested by a resolution supported by the majority of the totalmembership of each of at least one half of all district councils; or

  (c) if requested through a petition to the Electoral Commission by atleast one-tenth of the registered voters from each of at least two thirds ofthe constituencies for which representatives are required to be directlyelected under paragraph (a) of clause (1) of article 78 of this Constitution.

THE OTHER POLITICAL SYSTEMS ACT(2000)

http://www.ulii.org/ug/legislation/consolidated-act/262

Article 4. Petitions

A petition for approval of a politicalsystem under this act shall be in the form specified in the schedule of thisact and shall-

Be addressed to the commission;

be brought by a person registered as avoter on the national voters register; and

be supported by not less than one thousandother persons registered as voters on the national voters register.