The Maharashtra government has moved the court, seeking a direction to the CBI not to carry out any investigation with regard to two ''unnumbered paragraphs'' in the FIR lodged by the agency on April 21 against Deshmukh.
The CBI had lodged the FIR after conducting a preliminary enquiry following an order from the HC on April 5.
One of these paragraphs stated that the central agency in its Preliminary Enquiry (PE) found that Deshmukh was aware of the reinstatement of assistant police inspector Sachin Waze (now dismissed) into the police force and sensitive cases being given to Waze for investigation.
Waze is presently behind bars after being arrested by the NIA for his alleged role in the Ambani house bomb scare case and the murder of businessman Mansukh Hiran.
The second paragraph stated that Deshmukh and others exercised ''undue influence'' over the transfer and postings of police officers, as alleged by former Mumbai Police commissioner Param Bir Singh.
The state government claimed that these two allegations were not covered by the April 5 high court order.
Additional Solicitor General S V Raju, appearing for CBI, on Wednesday told a division bench of Justices S J Kathawalla and S P Tavade that the April 5 order did not impose any constraints on the agency.
''The high court in its order has said the agency shall conduct a preliminary enquiry within a period of 15 days and then decide the further course of action as per law,'' Raju said.
Senior counsel Rafiq Dada, appearing for the Maharashtra government, argued that the CBI went beyond the HC order.
Dada argued that the CBI has also sought documents related to a letter sent by IPS officer Rashmi Shukla.
''This (Shukla's letter about alleged phone tapping) has got nothing to do with the present case (corruption charge against Deshmukh),'' Dada argued.
The bench posted the matter for further hearing on May 21.