It have to depend on the occasion. To write down current managers as referrals meaning that new company will call up for verification. In this situations you need the cooperation from your current managers, otherwise it would seems to be a little uneasy for them to expect a call up from your new company. The way to make it appropriate would be giving to the person who you like to collaborate with in this case of retification of your current job. New company would just need to make sure your fact is straight up not a bluff as usually.