Juergen Mathies said CCTV footage was not good enough to identify sex crimes and police are relying on victims and witnesses to identify their attackers.
A total of 75 suspects have been identified, mostly North Africans who entered Germany illegal or sought asylum.
A major police investigation had to be launched after more than 1,000 criminal complaints were filed to police, with 467 alleging sexual assault, including rape.
Mr Mathies told the BBC: “The CCTV footage is not good enough to clearly identify sexual assaults.
“We can see some thefts but that”s all.
“We are relying on witness accounts and on victims identifying their attackers.”
His comments came as the first suspects to appear in court in connection with the December 31 attacks are due to go on trial today for theft.
Two Moroccans and a Tunisian man will appear in a Cologne court, three of 13 men arrested for theft.
Only one man, a 26-year-old Algerian asylum seeker, has been arrested on suspicion of sexual assault.
Wolfgang Albers, Mr Mathies” predecessor, was fired over the way he handled the exceedingly large number of assaults and robberies.
The incident was a turning point in Germany”s relationship with Chancellor Angela Merkel as she came under serious criticism for the country”s immigration policy which allowed 1.1 million asylum seekers into Germany in 2015.
Last week Cologne”s top prosecutor, Ulrich Bremer, was forced to angrily deny media reports only three of the New Year”s Eve attackers were refugees.
German media and authorities were initially accused of trying to cover up the Cologne attacks after it emerged they had deliberately tried to withhold the ethnicity of the alleged perpetrators.
Many had used an interview with Mr Bremer in respected German newspaper Die Welt to make the revelation but it later turned out certain news outlets and campaigners were working on the basis only people from Iraq and Syria counted.
Clearing up the confusion, Mr Bremer blasted: “The overwhelming majority of persons fall into the general category of refugees.
“They have various legal statuses, including illegal entry, asylum-seekers and asylum applicants. That covers the overwhelming majority of suspects.”