The Federation of Women Lawyers (Fida Kenya), International Commission of Jurists (ICJ Kenya) and lawyer Adrian Kamotho have sought to join the case, a move opposed by Mr Haji and Attorney-General Kihara Kariuki.
The Secretary of Prosecutions Dorcas Oduor and Mr Kariuki, through Emmanuel Bita, said Fida Kenya and ICJ Kenya have not demonstrated what expertise they have to assist the court in determining the case.
Ms Oduor argument was that DCJ Mwilu was properly represented in the case and the two organisations must demonstrate how they will assist the court to arrive at a just determination.
Through Ms Jeminah Keli and Mr Charles Mwongela, Fida Kenya and ICJ Kenya said their inclusion in the case was important because of the people they represent.
Fida argued that it has experience in protecting women’s rights, especially against discrimination.
She said the organisation has a legitimate interest in the matter, including protecting women in top jobs from being removed from office unfairly.
Justices Helen Omondi, Mumbi Ngugi, Francis Tuiyot, William Musyoka and Chacha Mwita directed the parties to file their responses in the application.
In the petition, Mr Haji wants the court to determine whether criminal prosecution of a sitting judge amounts to encroachment on the independence of the Judiciary.
Mr Haji also wants the court to determine whether criminal proceedings can be initiated against a sitting judge and whether before the commencement of such criminal prosecution, it is constitutionally necessary to remove the judge from office.
Other issues to be considered by the bench is whether the prosecution can proceed to institute criminal proceedings where the Judicial Service Commission has taken no action against a sitting judge despite knowledge and information about alleged criminal conduct of a judge.
The state had line up charges of abuse of office, failure to pay taxes, among others against Justice Mwilu but she obtained orders stopping the case pending the determination of the petition.
Ms Mwilu said the charges were deliberately brought to subject her to public humiliation and embarrassment.