The injectors have power always applied to the positive terminal. They are turned on by the ECU grounding the negative terminal. You might possibly have a short circuit to ground in the injector wiring.
Disconnect the injectors, and check the voltage on the terminals with the ignition turned on. One terminal on each connector should have 10v. The other should have nothing.
Turn off the ignition, and check the resistance to ground on the pin that didn't have voltage on it. It should show an open circuit. If not, disconnect the connector on the ECU. If it still doesn't show an open circuit, there is a short to ground in the injector harness. If the short goes away when the ECU is unplugged the problem is in the ECU.