The results were published by the Slovenian election commission on late Sunday evening after 99.9 per cent of the ballots were processed. Those are incomplete results and final and complete results are expected on Tuesday.
Slightly over 40 per cent of the eligible voters went to the polls for the referendum.
The result of the referendum is binding on the authorities.
As a result of the border dispute, Slovenia had used its veto power as an EU member to block Croatia's path towards EU membership. It lifted its blockade shortly after the agreement was signed by Slovenian Prime Minister Borut Pahor and his Croatian counterpart Jadranka kosor in Stockholm last November.