How to install crown molding to ceiling only
There's no reason that you can't fasten crown molding to ceiling joists... except that they'll probably only be present along half your walls. Unless you happen to have a hip roof design, the other half will run parallel to the joists and you probably won't have backing. In that case, trim screws with hollow-wall anchors may work, or nails backed up with project adhesive. 

It's also possible that you have a narrow ceiling backer at the corner (denoted below with #), to which you could fasten a larger backer (denoted with *). It might have the same angle that your crown molding does on the back. You'd then fasten your crown to that. 

##_________
|*/ /
|/ / 
| /
|/
|