I have an 05 KJ Renegade, and the yakima basketcase. I know the rails are JUST about far enough apart for the basket to fit inside the long way. (barely too close together to fit, however)
The web says that the dimensions are 26.5 x 38.75 x 2, so I'd say that from inside to inside the roof rails are probably around 38.5 or so, so maybe 40-45" on centers.
How are you planning on mounting it to the roof without crossrails? I'm fairly certain that the basket is skinnier than the rails, or too close to try to mount directly.
If you want a low-slung basket, check out the setup I have on my roof:
http://photos.jeffornot.com/Jeep/Roof%20Basket/p6160115.jpg
(note: the photo shows the basket the long way, with the 26.5" side between the rails. The rails are 50" thule bars, if that helps gauge size)
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Jeff 2005 Jeep Liberty Renegade
4x4, 6spd, Leather, Sunroof, trak-loc, skids/rails, hitch+shackle, hooks, Alpine/iPod, Thule, GPS, CB, Frankenlifted w/ 31" MTRs
Photos Cardomain