To achieve asymmetric layers of the lipid bilayer in a membrane, you would need to selectively flip some lipids from one side to the other. This would require an enzyme since the polar head groups of phospholipids would not be able to move through the hydrophobic membrane interior on their own. This would create asymmetry. This could be established at the Golgi, from which the asymmetry could be transferred to the plasma membrane by vesicles.
Work Step by Step
Lipids have hydrophillic and hydrophobic ends, and the hydrophobic ends cannot move through a hydrophobic interior. The energetics of this process make it totally non-spontaneous. Therefore, help from some kind of protein is needed. Asymmetry in the Golgi, but not in the ER, indicates that it is established in the Golgi. This asymmetry would move to the plasma membrane along with the lipids themselves and proteins being moved from the Golgi to the plasma membrane.