At which stage legality check is conducted?

CONSTITUTIONOF UGANDA (1995)

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

Article 11. Right of citizens to demand referenda

 (5) The Commission shall, on receiving apetition under this section, verify whether the petition has been dulysubmitted by a registered voter and supported by the required number ofregistered voters.

 (6) The Commission shall verify whether thesignatures are those of registered voters and that subsection (2) (b) has beencomplied with.

THEREFERENDUM AND OTHER PROVISIONS ACT (2005) 

http://aceproject.org/ero-en/regions/africa/UG/uganda-referendum-act-2005

Article 24. Challenging results of referenda

 (1) Any registered voter supported by thesignatures of not less than two percent of the total number of registeredvoters in Uganda may petition the High Court challenging the results of areferendum.