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A three-judge bench will Thursday hear another application seeking their recusal from cases touching on the impeachment process of Rigathi Gachagua.
Before that, the bench will first handle procedural issues of consolidation as cases touching on the impeachment have reached 30.
On Wednesday, Justices Eric Ogola, Anthony Mrima and Freda Mugambi dismissed an application by Gachagua and other petitioners who were challenging the validity of their appointment by Deputy Chief Justice Philomena Mwilu to hear some of the cases.
The bench said they do not find any fault in the DCJ assigning them the matters before the court, more so when the honourable Chief Justice has not raised any red flag.
It was their finding that the constitutional function of the CJ to assign benches, being an administrative function, can be performed by the DCJ when the CJ, for good reason, is unable to perform.
Separately, the High Court is expected to mention and give directions in a case in which Busia Senator Okiya Omtatah and two others challenged the rollout of the social health insurance fund.
Omtatah, Eliud Matindi and Dr Magare Gikenyi are also seeking an order to suspend any contract signed between the government, through the Ministry of Health and Safaricom Consortium for the provision of integrated Healthcare Information Technology System for Universal Healthcare.
They are aggrieved that the state is rolling out SHIF using subsidiary legislation which was annulled by the Senate.
They make reference to the Social Health Insurance (General) Regulations, 2024 and the Social Health Insurance (Tribunal Procedure) Rules 2024.
The trio claim that the state violated Article 113 of the constitution when relying on the annulled regulations.
"SHIF cannot be rolled out in the absence of enabling subsidiary legislation issued under the SHA Act and approved by Parliament to operationalize it," they said.