Yes, Arkham Asylum is mentioned often but has no ties to Batman. The name was used 1st by HP Lovecraft.
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Also this may help: http://www.yog-sothoth.com/wiki/index.php/Arkham
Arkham Asylum was first mentioned in "The Shadow over Innsmouth" circa 1931. Arkham itself is a fictional town made up by Lovecraft that is home to not only Arkham Asylum but also Arkham Sanitorium, The Miskatonic University and Miskatonic Medical School just to name a few. If you are interested there is a map of Arkham available online. Random House press has no trademarks on the name "Arkham Asylum" or any of its subsidiaries, so DC can and has used it many times. Cthulhu himself appears more times in pop culture comics unrelated to Lovecraftian lore than anything else, i.e Hellboy for example. The Cthulhu mythos is widely royalty free and the community enjoys people building upon the Lovecraftian lore. Hope this helps. 
@Ug interesting... Didnt know that, when i was looking about I found that DC Comics used it in some early batman comics. thanks for the heads up
Well...actually it was the other way around: Cthulhu-creator HP Lovecraft invented the town of Arkham back in the 20s, and DC Comics was making a reference to his stories.
