It appears that push does not accept wildcard refspecs. When calling git_push_finish (from LibGit2Sharp) with refs/heads/* it results in the following error.

results in:

Message=An error was raised by libgit2. Category = -3 (Error).
No such reference 'refs/heads/*'

Passing in the refspec "HEAD" does not seem to behave as expected, either.

git_push_add_refspec does not like short reference names either. Passing in push_me (when there is a branch refs\heads\push_me) results in the following error:

Message=An error was raised by libgit2. Category = Invalid (Error).
No valid reference 'push_me'