The two are unrelated, but they both have similar properties. We can disregard the mechanism of CO2 transport because as the CO2 concentration in the blood drops, the CO2 equilibrium: [ H+ + HCO3- <=> H2O + CO2 ] shifts to reverse the drop in CO2; that is to say, hydrogen ions and bicarbonate ions react to form water and carbon dioxide. For the purposes of this example, bicarb can be considered CO2.
I don't recall normal partial pressures so the values I'm about to use are arbitrary.
In normal breathing, you have a pCO2 in the air of 0.5, a pCO2 in the lungs of 3 and a pCO2 in the blood of 5, and a pCO2 in the tissues of 7. So CO2 diffuses out of the tissues into the bloodstream, and out of the bloodstream into the alveoli of the lungs - there is a continuous concentration gradient, if you like. This maintains the pCO2 in the blood within normal ranges (4.5-6kPa IIRC).
The pCO2 in the lungs is dependent on how rapidly and how deeply you breath - e.g. are you completely replacing the lung air with atmospheric air? And how frequently are you doing this?. Obviously, the more quickly you breath, the more atmospheric air you will get in your lungs, and so the pCO2 in the lungs will lower towards 0.5. The same applies with taking deeper breaths. Enter hyperventilation:
In hyperventilation, you reduce the pCO2 in the lungs to 1. This increases the rate at which you clear CO2 from the blood - instead of there being a concentration gradient of 2 (pCO2 in blood = 5, pCO2 in lungs = 3), there is a concentration gradient of 4 (pCO2 in blood = 5, pCO2 in lungs = 1). The rate of CO2 clearance has doubled, and if you keep hyperventilating for 30s, the pCO2 in the blood will drop to 3, and the pCO2 in the tissues will undergo a similar drop, to 5. Basically, a new equilibrium has been set up, with the baseline CO2 level lower than the previous baseline, so CO2 concentrations throughout the body have dropped accordingly - you are breathing out CO2 faster than you are producing it.
With me so far?
Now, supposing we were breathalysing for CO2 instead of alcohol. Ordinarily, we'd breath out a pCO2 of 3. But because we've been hyperventilating, our lung pCO2 is down to 1, so we're only going to breath out a pCO2 of 1. This gives a lower reading on the breathalyser. If you stop hyperventilating, you will no longer be breathing out CO2 faster than you are producing it - you will begin to produce it faster than you breath it out, so concentrations will rise to normal.
It is essentially the same process with alcohol. Ordinarily you will breath out x concentration of alcohol, and that will correspond closely to your blood alcohol levels, because the higher the alcohol concontration in your blood, the more rapidly alcohol enters the lungs. Hyperventilating will lower the alcohol concentration in the lungs and in the bloodstream, temporarily, and may enable you to pass a breathalyser test because you will be breathing out less alcohol.
That all make sense?