Kumar was summoned for questioning at 10.30 a.m., but he sent a letter seeking a week's time before he could present himself for the questioning, stating "personal reasons".
Two CID officials went to the Central Bureau of Investigation office at Salt Lake and delivered the letter.
The development came hours after late on Sunday, the West Bengal government reinstated Kumar as CID Additional Director-General, a post from which he was shunted out by the Election Commission and sent on central deputation on May 15.
The state government in a notification said Kumar was being reinstated as the model code of conduct had expired.
The CBI on Sunday served notices on the former top cop at his residence and his office summoning him to be be present at its Salt Lake office at 10.30 a.m. on Monday for interrogation in connection with the Saradha ponzi scam.
The CBI team issued the notices after they failed to locate him. It also issued a lookout notice for the senior IPS officer and alerted all airports to scuttle any effort on his part to escape abroad.
The Supreme Court on May 17 had withdrawn the protection from arrest granted to Rajeev Kumar by its February 5 order. It, however, had given him seven days time to approach a competent court for relief.
Kumar last Monday had moved the apex court seeking extension of the protection from arrest in view of the lawyers' strike in Kolkata, but the court had rejected it.
( With inputs from IANS )