Yoon failed to attend a hearing he was summoned to on Wednesday and gave no reason for his absence.
Prosecutors earlier this week had ordered Yoon to appear for questioning or face possible arrest, but they have handed the case over to the CIO.
CIO chief Oh Dong-woon told parliament on Tuesday they were also “reviewing” whether to issue an arrest warrant.
Yoon has been suspended from his position, and the Constitutional Court on Monday began proceedings to determine whether to uphold his impeachment. It has around six months to rule on the matter.
The court has been requesting documents related to the martial law declaration, but they have now been returned undelivered three days in a row.
“The attempt to serve documents to the respondent, the president, failed. Meaning that they could not meet him,” said a spokesperson for the court.
“We are reviewing other options,” she added.
Former President Park Geun-hye was impeached under similar circumstances to Yoon, but she was investigated after the constitutional court removed her from power.
