A closure assembly (20) that includes a cap or overcap (28) and a fitment (24) for a container is provided wherein the fitment (24) has a laterally projecting shear member (40), and the overcap (28) has an aperture (74) for initially receiving the shear member (40) when the overcap (28) and fitment (24) are in an initially assembled orientation or condition. The aperture (74) and the shear member (40) cooperate in the initially assembled orientation such that when subjected to a flow of a sterilizing gas, turbulence is created in the sterilizing gas flow to enhance sterilization of the combination. The closure assembly (20) may, instead, or additionally, be provided wherein the overcap (28) has an elongate, hollow plug (58) for establishing a first seal between the fitment (24) and the overcap (28) in the initially assembled orientation, and the wherein overcap (28) has a skirt (50) for establishing a second seal between the fitment (24) and the overcap (28) in the initially assembled orientation.