Makueni MPs Kisoi Munyao and Richard Makenga have demanded the arrest of Governor Kivutha Kibwana over the burning down of the county assembly.
They pointed out the governor's assertion that he had prior information on the imminent arson and had told the Speaker about it in December.
"He has information that no other Kenyan has," said Mr Munyao at a press conference at Parliament.
Mr Makenga said the statements made by leaders from the county should not be taken lightly and should be followed up by criminal investigators.
"The governor is the custodian of public interest in the county and when he says he told the Speaker about it, it is an abdication of his job because he should have contacted the security agencies to prevent the arson," said Mr Makenga.
The governor had last year offered to resign after differences between him and the county assembly escalated to the shooting of several people.
An attempt spurred by the public to dissolve the county government was rejected by President Uhuru Kenyatta.