Disconnect both speakers from the amp. Set your multimeter to measure resistance (which is what you have it set to). Measure the resistance across the tweeter on both speakers. If the resistance isn't approximately the same, then you have a bad driver (or bad connection to the crossover).
You could just try measuring the non-working speaker, but I don't know what influence the crossover will have on the reading, so you'd need to disconnect the tweeter from the crossover first. If you want to do this, you should get an impedance in the 4 to 8 ohm range. If it measures as an open circuit (often shown as --- or OL), then the tweeter has a broken connection somewhere inside and probably needs to be replaced.