This was the fourth car-free day initiative of the AAP government to curb vehicular pollution.
Sisodia's accusation came as he noticed cars being allowed to ply on the 'car-free stretch' from Vishwa Vidyalaya Metro Station to Chhatrasal Stadium.
"I am seeing that cars are running on the car-free stretch. Police should shoulder some responsibility (to make the event a success). We are even ready to give you (police) the credit of the success of odd-even.
The Deputy Chief Minister said police should also participate in such events and if they get an order to make the programme a "failure", they should not obey the orders of their seniors.
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Delhi Transport Minister Gopal Rai said that he got a letter from Special Commissioner (traffic) stating that volunteers will not be allowed to manage traffic during 'Car-Free Day'.
He also said that the government will start a plantation drive from the next 'car-free day' across the national capital which will be held in South Delhi.
Such an event is held on the 22nd of every month.
Sisodia said government has taken several steps to make the city pollution-free,
The last 'car-free day' was organised in Laxmi Nagar.
Rai had alleged that Delhi Police did not allow plying of buses on the car-free stretch. He had taken up this matter with senior police officials and registered his objection.