Indeed, this is a tricky question, as the label includes terms such as "Fencerow" and "Noncrop Non-Agricultural Area."  To avoid any uncertainty, I called the Oregon Department of Agriculture, and they informed me that for a number of years they have been interpreting Crossbow labels as NOT including residential sites and have cited people on numerous occasions for using Crossbow on residential sites.

That being said, there are other products containing similar ingredients that may be effective on ivy.  If it is practical to cut and physically remove the ivy, there is a "cut vine and stump killer" product with a dauber attached to the lid such that you paint it, undiluted, on fresh cuts (must be fresh to be effective).  If there is too much for that to be practical, you may choose to cut it down and then treat the re-growth with an herbicide.  Cutting it will weaken it, and treating only the re-growth will use far less herbicide than treating all of the growth.  I don't make a habit of recommending specific products, but there is one that is likely to be more effective than the others: Roundup brand brush killer.  I say this because it contains two ingredients: glyphosate and triclopyr.  This product is similar to mixing "Roundup" (glyphosate) and Crossbow (which contains triclopyr, along with another, relatively weaker ingredient).  Also, the Roundup brush killer contains a surfactant, which is critical when applying to ivy due to the thick, waxy cuticle that causes water-based materials to bead up and run off.  If you use this product, keep in mind that it will kill any green vegetation it lands on.  Also, triclopyr (whether from Crossbow or another product) can be taken up by roots, so nearby plants can be affected as well.