Commissioner Drew Harris refused to be drawn on the incident involving a PSNI jeep at Garda Headquarters.
During the incident a PSNI armed protection car in which Mr Harris was a passenger crashed on a bollard in Garda Headquarters.
Questions have been raised why armed PSNI officers were used to ferry the garda boss into the Pheonix Park Headquarters.
Harris insisted that protocols were in place and had been followed.
He said: “If I step back from the specific incident you are referring to and say that all protocols that are in place for cross border movement are adhered to.
“They have been in place for six years and these are in place. I am not going to answer that question directly because it does impact directly on my security and my security arrangements.
“This matter relates to my own security and the security of my family and I don't wish to comment any further.
“I am not going to answer that question directly. By implication it draws me into that as well.
“People don't know about my security arrangements because I don't publicise them and that's probably the safest for myself, for my family and for those who accompany me. People make presumptions on my security."
