Abstract: The catheter assembly is provided with a conventional catheter which extends from a hub. In addition, a tube or blunt needle is mounted within the hub coaxially of the catheter and is provided with an elastomeric valve over the open end. The elastomeric valve is formed by a pair of rubber sheaths, each of which has a closed end for sealing the tube against a back flow of blood. The sheaths can be pierced by a needle in order to perform a venipuncture while re-sealing upon removal of the needle. The catheter assembly may also be connected with a male luer connector in a manner to push the sheaths over the tube so as to expose the lumen of the catheter to the connector.