A 1984 CRX will have a fairly complex carburetor on it. Carbs do not react quite the same way to cutting the ignition that fuel injection does. If you cut the ignition while the engine is at high RPMs, it will continue to draw air through the carb into the engine, which will bring fuel along with it. There will, however, be no spark to light that fuel so it burns. There is some potential for loading up the exhaust with unburned fuel, which will then light off when the next very hot slug of exhaust comes along after the engine is running again. That can damage your catalyst.
Bump-starting faces similar problems if it takes a while for the engine to start running, or if you try unsuccessfully several times.
Based on that, I would let the engine come down to idle before shutting it off as Ryland suggested. I would also try to limit bump-starting to occasions when I was pretty sure that the engine would start running very quickly. Otherwise, I would use the key to start. (Note that Wayne over on the cleanmpg forum only does key-starts on his Accord, which is still running strong at over 300,000 miles I think!)
I would not be certain that the catalyst is dead. The original one on my 1990 CRX seemed to be working pretty well still as of last year when I sold it.
-soD
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