A bench of justices Badar Durrez Ahmed and Siddharth Mridul refused to vacate the stay despite the Delhi Police contending that non-availability of fresh uniforms would lead to an embarrassing situation.
The counsel for Delhi Police further contended "why should they suffer".
"Let them (Delhi police) open the bids as the dresses are required ahead of the US President's arrival next year. The new dress code is exclusively meant for the security personnel deployed on January 26, 2015.
The court said why they should lift the stay and instead the petitioner Fashion Fusion be allowed to participate in the technical bid and if it finds them incompetent, their proposal can be turned down.
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Fashion Fusion contended that it had been providing the shirts and trousers to Delhi Police in the past but in this year's tender there was the additional requirement of getting a certificate from a mill owner that the company has requisite material.
The petitioner-company has said that the technical bids have been opened and the samples of other bidders have been sent for testing but not its own.
The court has sought a response of Mafatlal by December 12, the next date of hearing.
According to the norms, all policemen from the rank of constables to inspectors, including the station house officers, are entitled to a new pair of shoes and clothes every two years.