The restriction will apply to cases where the allegation can be linked to a public servant's official work.
It will apply to serving as well as former public servants.
The Rajasthan government had made the changes to the criminal procedure code by an executive order, or ordinance, on 7 September last month.
On Monday, the ordinance is expected to come up for approval of the state assembly, where the BJP has 162 of the 200 seats.
It is not clear if the changes will impact the power of the police to register cases against public servants as well.
But if the police does not act on a complaint, say against a minister or lawmaker accused of corruption, a private citizen has the right to go to the local court to seek orders for a probe.
Now, before the court gets to decide if the complaint merits a probe, the law says the government will take get six months to decide if the court should hear the complaint at all.
If the state government does not get back to the court with its approval within six months, it will be deemed to have given its sanction. The law does not require the government to give any reasons.
The changes are broadly patterned on restrictions proposed in the Prevention of Corruption Act pending in parliament's Rajya Sabha. The Manmohan Singh government had first moved similar changes in 2013 to the anti-corruption law, ostensibly to protect honest public servants.
The Rajasthan government's version goes a step further and outlaws reporting any information that ends up disclosing the identity of the judges or public servant facing accusations unless the government has vetted the case. Journalists can be sentenced to two years jail for violating this rule.
The Supreme Court had last upheld the right of a private citizen to set the anti-bribery law in motion in the January 2012.
In this judgment delivered on a petition by BJP leader Subramanian Swamy, the court had ruled that the constitutional right of a citizen to file a complaint "should not be burdened with unreasonable fetters".
Read the full text of the ordinance: