Matt, you might be able to use the dryer connection. Electric dryers are usually 240, washers usually just 120. You could make a plug cable to adapt the dryer plug to the plugs required for the unit. In looking at the specs, the main unit needs 3.9 amp at 240. You might be able to source a transformer to run that part, might not be cheap. The dryer side of the CP51 needs a lot more current and a 240 circuit would be the best choice.
A lot of this has to do with the wire gauge in the wall. You might want to talk to an electrician and get some estimates. Existing wiring dosn't usually plan for equipment like the CP51.