Background check packet, and address question...??

[emm74]

list both. They aren't going to be checking to see if you changed your address at Motor Vehicles but it's certainly likely the second address will pop up on your record.

[KellyXY]

Usually when they ask for past addresses on a typical background check they're trying to identify places to search for criminal records, etc. To be compliant with the spirit of the question, you probably should list anywhere you've been for a significant amount of time within the background check period (e.g. the address where you stayed on vacation probably doesn't need to be included if you'd have no record there, but if you were a college student in a different town than where your home was you probably should include that). They generally don't care about the exact addresses so much as that you identify every city/county/state/etc. that you could have a criminal record in. The serious issue would be if you end up concealing a record because you didn't disclose where it was located and the background check didn't reveal it (which would be true even if the crime was committed "away from home").

ETA: In other words, another address in the same town that pops up probably won't be an issue because that wouldn't provide any more useful information to assist in the search, but an undisclosed address from another city (and especially another state) would probably raise eyebrows. (Some criminals try to move away from where they committed their crime(s) to make it harder to find their record(s), and the former address inquiry/search helps combat that.)