In-universe, it's a slang term for someone who is acting in a way that is beyond understanding.
Note that technically (again, in-universe) it does mean "alien;" in Tripoint the Downers are referred to as "eetees." Tom's internal monologue:
Even so, you weren't supposed to [Downers], trade with them, touch them, or 'impede them in any way whatsoever, under penalty of law and a substantial fine...' Which was probably for everybody's protection, humans as well as the eetees.
It doesn't precisely mean "crazy" though; in Cyteen the word "crazy" is used all the time; "eetee" is stronger than "crazy." Justin to Yanni:
"I'm saying it's solved here. I'm saying I've got it. You critique my designs, then. You want to tell me I'm crazy, show me where I'm wrong."
Whereas an alpha azi, looping on its own mind-state can go completely beyond normal understanding:
And once an Alpha stops re-analyzing his input and starts outputting only, he's gone completely eetee.
One theme that shows up in many of Cherryh's stories (like Forty Thousand in Gehenna, Cuckoo's Egg, Foreigner, Chanur, and others) is that aliens are alien and that it may be impossible to actually really understand one another. "Eetee" is used to describe someone who has gotten to a point where their thought processes are alien to another human.
In Rimrunners, Yeager considers the possibility that NG might "go eetee:"
But NG waited, he sat there on this ship that saner crew like Parker and Merrill were complaining about and ready to duck out on, the whole crew ready to mutiny if they hadn't done it already out there—and they were sitting still on her say-so, too, she didn't know why. They might be worried about the consequences of guessing wrong, but if NG decided to go eetee he didn't always think five minutes down the line, damn sure he didn't play team with anybody—
While at the same time, other people are just "crazy:"
"I tell you," she said, "they're all crazy."
Note that this is on the other side of the Union/Alliance divide, so this isn't just a regional dialect issue.