"The party has issued show cause notice to Taslimuddin," RJD state unit president Ramchandra Purbe told PTI.
Purbe, however, did not specify the time-frame within which Taslimuddin has to reply.
He also refused to answer whether any show-cause notice has been given to senior RJD leader Raghuvansh Prasad Singh, who too has been critical of the Chief Minister.
RJD sources said the controversial statements were indirectly helping BJP.
The party's decision assumes significance in the backdrop of the fact that its ally JD(U) yesterday took strong exception to the statements made by Raghuvansh Prasad Singh and Taslimuddin and demanded action against both leaders.
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Taslimuddin had trained his gun once again at the Nitish Kumar government yesterday, urging the RJD boss to snap ties with JD(U).
He had said the chief minister should first set things in order in Bihar before undertaking a nation-wide campaign on prohibition.
Soon after the meeting of the state and central parliamentary board of RJD here Friday, both Raghuvansh and Taslimuddin had attacked the Nitish Kumar government.
On an earlier occasion as well, Taslimuddin had said Nitish Kumar was not "PM material" and was "daydreaming of becoming the prime minister".