Here is the relevant definition (copied and pasted from the AMA CL General Section--so it at least should apply to all CL unless other specific rules supercede it), and as Crist says, there is nothing on actual dimensions. (That surprised me too!). But at least there is a definition. I suppose a profile contest which is AMA sanctioned, at least can have a definition of what a profile is!
10. Profile Definition. The fuselage of a
profile model resembles that of a
conventional airplane in the side
(profile) view and appears as a thin flat
sheet in the plan (top) view. The engine
shall be completely exposed from the
mounting lugs to the cylinder head and
shall not have any type of fairing.
Additional reinforcements such as
plywood nose doublers and cheek cowls
on the opposite side of the engine (for
side mounted installations) are
permitted. Cheek cowls may extend
from the prop drive washer to a point 25
percent of the root chord back of the
leading edge at the root, and may be
faired in. In the case of an inverted or
upright engine installation, the engine
mounts may protrude from the fuselage
sides but may not be faired in.
By the way, having the official version of the rulebook in electronic version actually makes it easier to find stuff like this. Since you are reading this on a computer, just go to the AMA site, click on the competition regulations, then do a search (in this case on "profile"). This is easier than a book primarily because this info is usually spread over a number of places in the rulebook, so manually searching makes it easy to miss these little "nuggets".
On the other hand, it is useful to download the sections, so in the future, when a new rule slips in or out, you will have some reference to know that you haven't lost your mind! At least as of this year, they put dates on the pdf files!