I would first check with a good chevy dealer.  He could look up the VIN number and see if any recalls were done.  After that I would get ahold of somebody at the NCM (National Corvette Museum) in Bowling Green Ky.  I am sure they will have records there.  They have none for my 1981.   She was built in St Louis and all records are gone to never, never land.

Any factory recall work that has been performed would have had a decal/sticker affixed under the hood somewhere denoting the recall program number, and the date of the repair. Sometimes those decals don't survive very well, and sometimes it looks like the outside of a Nascar vehicle!
"Recalls" are only done for safety and/or emissions related issues. You'll not find a recall for a molding that is falling off, or wrinkles in the carpet.
So....have a good look under the hood for any decals/stickers that will specify a recall repair that has been done. Not all cars were repaired under a recall...

Hex,

There were 6 recalls for the '89 model year. 2 were NHTSA mandated, and one was a campaign for paint problems.
892213B10- White paint discoloration
90C09A5-  Parking Brake Inoperative
89C173D-  Rear wheel tie rod could fracture
89C17A3D-  Updated rear wheel tie rod could fracture
NHTSA90V032000- Rear tie rod defect
NHTSA91V143000- Seat belt retractor defect

btw...I have access to all of the recalls/TSBs here at the shop, if anyone is looking for info.
There are over 100 TSBs for the 1989 model year...

What excellent information and web site.  We could hire ourselves out to answer corvette questions!!

Note to myself, next time I am in Ft Worth I gotta look Joel up !!

Did all this info help. Frank??

Yes, this was a great help.  Finally got Chevy to tell me that there are no open recalls on my car.  Now all I have to do is get her up to snuff on services...  Thanks everyone... 

Frank, Highly reccomend the book 101 Projects for Your C4. It sounds like upgrades but is primarily maint projects. I use it extensively when working on my '96 LT4.