The 51 members were accused of allocating the funds for the second consecutive time during a debate on the 2015/2016 financial year in Parliament on Wednesday.
The issue was raised by Gem MP and Deputy Minority leader Jakoyo Midiwo, who said the MPs have received Sh40 million for their constituencies.
In the previous financial year, the MPs reportedly allocated their constituencies Sh3 billion.
Nandi Hills MP Alfred Keter pointed out that “his neighbour” Stephen Bitok of Mosop, who sits in the committee, had been allocated Sh40 million to set up a secondary school.
Midiwo claimed the MPs in the committee were getting preferential treatment from the Education and Transport ministries.
They have “awarded themselves strange monies for a second time”, Midiwo said.
He claimed the “strange allocations of up to Sh20 million were for infrastructure, bursaries and Early Childhood Development, which is a devolved function”.
Midiwo said there has been inactivity in some areas but “in the neighbouring constituencies of these members, there is activity worth millions of shillings”.
He added that the bursary distributed through the District Education Board had not been forthcoming in some constituencies in the last financial year.
The Minority leader said it was illegal and unconstitutional for MPs to use their positions in committees for personal benefit.
“What structure are they going to use to disburse that money? We know they arm-twisted the Cabinet Secretary (Treasury) to give into an illegality,” the People Daily quotes him.
Midiwo asked Deputy Speaker Joyce Laboso to organise a closed-door meeting to discuss the issue.
Saying such a meeting would yield discussions and clarifications, Laboso said an informal one would be arranged after discussions with the Majority and Minority leaders and the office of the Speaker.
Budget committee chairman Mutava Musyimi said he was not in the chamber when Midiwo raised the matter, but supported the ruling by the speaker.
The money for all 47 counties, channelled through the County Development Fund, and was meant for projects identified by locals and presented to the committee.