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An issue that a lot of real estate agents have told me that the home inspectors are finding and reporting on home inspections is double-tapped breakers in the breaker box.
First we should define exactly what a double-tapped breaker is; when two or more wires are connected to the hot terminal on a breaker that is not designed for more than one wire, you have a double tapped breaker. Essentially you have two lines running out of one breaker.
Now whether this is a mushrooming event or something the home inspectors have just discovered and are looking for and using as justification for their services or not remains undecided. A few homeowners report that they added nothing to panel box and it wasn't caught when they bought the house.
What you choose to believe or not believe about home inspectors isn't the issue. Double-tapped breakers are a violation of the NEC code unless the breaker is rated for more than one conductor. I know for a fact that some Square-D breakers are rated for two wires. I also know it is a clear violation of code if it isn't rated that way.
And more to the point, I agree that it can potentially be a problem. If the device was designed for one wire it may fail or the connection may fail when more than one is used. Just because it has worked for some time does not mean that there isn't a loose or potential loose connection there.
As always, turn off the juice before you play with wiring. In this case since you are working in the panel box, turning off the main breaker or better yet the external disconnect is the correct choice. Do keep in mind that the main lugs at the top of the panel box may still be hot, even with the main breaker off. It is always a good plan to test a wire for juice before you grab hold of it no matter how sure you are that the power is off.
So what can you do? If you aren't having any problems with the circuit being over-loaded the fix is really simple assuming the two wires are the same gauge. Simply disconnect them from the breaker, add a pig-tail of the same gauge wire, connect the three wires together and secure the pig-tail to the breaker. A splice inside the box is allowed and you now meet code and have satisfied the home inspector for about a dollar. Not many home repairs you can do for a dollar.
If the wires are not the same gauge you will need to make sure the ampacity of the breaker matches the gauge of the smaller wire and perform exactly the same task of splicing the two wires to the pig-tail and connecting the pig-tail to the correct sized breaker. Personally I would use the larger gauge wire for the pigtail portion since wire is cheap and bigger never hurts anything.
Our article Selecting the Proper Wire Size can help you with wire and breaker sizes.