The opposition party accused BJP ministers and leaders in the state of being involved in the scams, and asked Shah, who is on a visit to MP, to reply to corruption charges against the Shivraj Singh Chouhan government.
The BJP has refuted the charges as "baseless and false" and said that it did not need a "character certificate" from the Congress.
Leader of Opposition in the assembly Ajay Singh of the Congress claimed the multi-crore scams had surfaced during the last 12 years of the BJP rule.
"Shah should come out with his reply to these scams," he demanded.
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The Congress leader said corruption was at its "peak" in Madhya Pradesh, but the BJP was giving an impression that all was well in the state.
The state goes to the polls in 2018.
Shah arrived here yesterday on a three-day visit to Madhya Pradesh for meetings with the BJP workers and office- bearers besides participating in various programmes as part of his 110-day nationwide tour.
Reacting to the allegations, Madhya Pradesh BJP general secretary V D Sharma said that his party did not need a "character certificate" from the Congress.
"The BJP has given corruption free government in MP. Prime Minister Narendra Modiji has taken a slew of drastic measures to eradicate corruption and no charge of corruption has been levelled against his government in last three years," he added.