Mr Kejriwal retaliated brusquely; pointing out that Mr Kumar's own party is in power in Himachal Pradesh, so sharing the information is the BJP's responsibility.
Last week, Mr Kejriwal and lawyer-activist Prashant Bhushan whipped up a political controversy by alleging that Priyanka's husband received interest-free loan and discounted apartments in posh projects built by real estate giant DLF.
Priyanka Gandhi Vadra is constructing a house at Chharbara, 12 km from Shimla. An acre of land was bought by Mrs Vadra in 2007 after the-then Congress government relaxed rules in her favour. Land in Himachal Pradesh can't be bought by non-residents under the state's laws.
The land for Priyanka was apparently given in two installments, the second was released by BJP chief minister Prem Kumar Dhumal, who is now in power.
Mr Kumar, a former chief minister, though has deliberately taken on the BJP government in the state while making his demand for the probe. Analysts say that Mr Kumar's googly is meant to hurt the incumbent chief minister Mr Dhumal, who is going to be fighting elections in the next two months. The BJP has been handicapped by in-fighting, especially between the Dhumal and Kumar camps for the last few months.
Mr Kejriwal, who launched a political party last week, said today in an emailed statement, "Shanta Kumar is saying he does not have information. We don't understand this. He can find this out very fast as his party is in power. We appeal to Shanta Kumar and Chief Minister P K Dhumal that they tell the public whether Priyanka has any property in Shimla as is alleged. We also know that no outsiders can buy property in Himachal without the state government's permission. If this is true, when was Priyanka Vadra given permission to buy property in the state and which government gave it."
In an attempt to make it clear that his new party does not side with any existing political party, Mr Kejriwal's statement added, "We want to bring their attention to the fact that BJP is also involved in this loot as any other party is. The same story is coming out in other states also where BJP is in power."
(With inputs from agencies)