Never direct a complaint to the top; a serious offense is to “cc” a person’s boss on a copy of a complaint before the person has the chance to respond to the complaint.  

If you have a complaint, first take it directly to the individual in a straightforward manner and give him or her a chance to know about it and work it.  To send a complaint to an individual and at the same time to “’cc” that individual’s boss can be counter-productive.  I have found that most times the problem may not get solved and you’ve ended up alienating someone you will need to work with later.

It is usually better to let the individual know.  Then, if you are not getting support, you can let the supervisor know.  AT the same time – and this is very important – it is essential that everything be done in a way that adheres to all rules and regulations, reflecting the utmost integrity.  

On the positive side, if you have something wonderful to say about a peer, they by all means copy the boss.  As it is said, “Praise in public, admonish in private.”