Singh, along with his lawyers, appeared before the Additional District and Session Judge Kashinath Singh, a day after the court issued a non-bailable arrest warrant against the former chief minister, who is an accused in the case, for not turning up before it.
The court granted bail to Singh after he furnished a bond of Rs 30,000. The prosecution did not oppose his bail.
A 169-page supplementary charge sheet was filed yesterday in the case which pertains to alleged irregularities in recruitment in the state Assembly Secretariat.
Singh was accompanied by MP Congress President Arun Yadav, former Union Minister Suresh Pachouri and his lawyer Vivek Tankha.
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Tankha pleaded before the court that his client is a renowned politician and he failed to appear before the court yesterday as there was an important event in Ujjain where his presence was essential as it was planned in advance.
"My client respects the court and has no intention to run away from it as he has already recorded his statement on the issue before the police," Tankha told the court.
Tankha also said that Singh is a Rajya Sabha member and a former Chief Minister who enjoys a clean image and deserves to be released on bail.
As the prosecution did not raise any objection to Tankha's submission, the court granted bail to Singh.
A large number of Congressmen had also gathered in the court premises.
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"It was a totally politically motivated case and a fallout of Vyapam scam as I have targeted (Chief Minister) Shivraj Singh Chouhan in the matter," Singh later told reporters.
Tiwari had filed the affidavit on the behalf of former Speaker Sriniwas Tiwari, one of the accused in the case.
"It is apparent that no grounds emerge for conducting any further inquiry into the charges, in case the preliminary inquiry report is accepted in its existing form."
He said the case against him lacked substance.
"After going through the affidavit, it is absolutely clear that there is no ground in the matter.
"I agree with the opinion given by the Principal Secretary, General Administration Department in which he has stated that the report which has been submitted contains only introductory facts and it does not show any charges which may warrant for forwarding it to Central Bureau of Investigation," the Congress general secretary said.
"The excel sheet (allegedly implicating Chouhan) was tampered with to benefit him and I demand the CBI, probing the Vyapam scam, to examine it (sheet) and take action against me if it is not (found to be) doctored," he said.
Singh also asked the agency to "probe" the wealth of the MP Special Task Force (MPSTF) officials who had earlier investigated the case.
He alleged that the officials "extracted money from those allegedly involved in the scam".
Singh said the non-bailable warrant was issued against him though his lawyer had appeared before the court and sought another date as a programme organised by him in Ujjain could not be postponed.
Referring to the warrant, Singh said since he always remains under "protection" of MP Police, "the question of my running away does not arise".
"I don't have any personal fight with Prime Minister Narendra Modi and Chouhan. I only have ideological differences with them which will remain forever. But, by creating problems for me, I think they are dialling a wrong number," he said.