There was an episode synopsis about a Law & Order crossover between CI and SVU where Logan appears on SVU, but it never happened.
A few years ago there were plans for a massive crossover of *all three* L&O shows, involving a terrorist attack on NYC, but it was quickly cancelled after 9/11 took place. To this day I don't think any crossover has involved all L&O shows, and I don't think CI has ever had one.
Me, I would have liked a L&O/Sopranos crossover: Jack McCoy goes up against Tony Soprano.
Actually, that might work better now: Set *Michael Cutter* after Soprano. Cutter would make mincemeat out of all of those guys.
There's already been a Who/Trek crossover, in a sense. It was called The Doctor And The Enterprise
. The 4th Doctor shows up on the Enterprise
and helps them battle the...shit, I can't remember who, I think it was the Rutans or the Sontarans (the Doctor determines that they are in his universe, after pointing out some differences between the two - in Trekverse, Gallifrey does not exist as its sun supernovaed quite a long time ago, and in Who, Vulcan destroyed itself in civil war). One thing I thought was weird is that in this story, no Trek character is ever identified by name - they're just The Captain, The Engineer, The Physician, etc.