If the axe is to be used just for splitting then it really doesn't need to be razor sharp at all because you're not cutting into the wood. You're using the axe as a wedge to drive the fibres of the wood apart. Some would say that a slightly blunt axe is actually better for splitting as it won't stick in the wood or the chopping block.
However, if you're using it for chopping, cutting, carving or anything else other than splitting then it'll need to be properly sharp.
Hold up a piece of printer paper by one corner and try to cut into it by 'swiping' the axe across it. If it makes a good clean cut without tearing the paper then your axe is as sharp as you'll need it.
The best thing is to try it out. If you can split different woods easily with your axe then that'll do.
''It is poor manners to ask someone for the loan of his axe.
It is worse to use it without permission.''
- Mors Kochanski