The court had earlier refused to accepted the closure filed by the probe agency in the case in 2008 and had asked the CBI to further investigate the matter.
However, the CBI had again approached the court saying "allegations levelled against Gandhi and two others could not be substantiated".
Senior BJP leader Maneka Gandhi is now the Women and Child Development Minister.
The FIR alleged that Maneka, in conspiracy with Siddiqui, had sanctioned a grant of Rs 50 lakh to GRWT from MAEF in an irregular manner to construct a nursing college building at Pilibhit in Uttar Pradesh and caused undue favour to Sharma.
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CBI alleged that further an amount of Rs 10.40 lakh was sanctioned to GRWT by S K Verma, the then District Magistrate of Pilibhit, from Maneka's MPLADS (Members of Parliament Local Area Development Scheme) funds for purchase of two ambulances and the fund was released to Ramakant Rampal, the Managing Trustee of GRWT.
"during the course of further investigation, the allegations levelled against Maneka Gandhi, Dr F U Siddiqui and Dr Vijay Sharma could not be substantiated."
"It is, therefore, prayed that the closure report dated December 30, 2008, collectively read with this report, may kindly be accepted," it said.
The FIR in the case was lodged for the alleged offences under section 120-B (criminal conspiracy) read with section 420 (cheating) of the IPC and under relevant provisions of the Prevention of Corruption Act.
In its closure report, CBI said that the trust had purchased two jeeps with ambulance fixtures on September 15, 2003 for Rs 9,85,008, while the balance amount was returned to the government exchequer as per the terms of sanction.
"Investigation further revealed that the DM, Pilibhit, approved purchase of two Mahindra Voyager ambulances. A cheque dated July 27, 2003 amounting to Rs 10.40 lakh was received by GRWT for purchase of Mahindra ambulances AC Euro-II.
"Since production of this model of vehicle was temporarily stopped, the company offered to sell Mahindra DI ambulance which according to the company was rugged, reliable and easily serviceable in semi-urban and rural areas," it said.
It said the funds released by both MAEF and district administration, Pilibhit, have been fully utilised by the GRWT for the purposes.