Liu said this week that a contractor hired to overhaul the system may have received millions in unjustified payments.
Bloomberg said Friday on WOR Radio that the contract was registered with Liu's office and the budget was approved there. He questioned if Liu even read the contract.
Bloomberg said, "It's pretty hard to answer something as stupid as this charge."
Liu has asked prosecutors to investigate whether there was any criminal fraud associated with the contract.
After the criticism, Liu sent Bloomberg a letter accusing him of attempting to "confuse the public and shirk responsibility on this issue."
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