Here is a link to The Single UNIX Specification Version 2. Which is 98% conformative to POSIX (as SUSv2). But I would not expect the behavior in this matter to have changed.
It talks about the dirname call.
EXAMPLE
        "/usr/lib"      "/usr"
        "/usr/"         "/"

Deriving from this I would assume POSIX accepts trailing slashes on a directory.

link: http://www.opengroup.org/onlinepubs/007908799/xsh/dirname.html

Best regards
Per-Olof Pettersson