How do I get a tmux session's base directory?

I have been using tmux for a few months, and there is one thing that always bothered me: when I type cd into my shell, I get moved into my home directory (this is the standard behavior of cd, so nothing unexpected). What I would like to have is that I get into the current tmux session's base directory, and this could probably easily be implemented via a shell function:

cd () {
   if [ $# -eq 0 ]
   then
      command cd $TMUX_BASE_DIR # fictional environment variable
   else
      command cd $@
}

However, I have not found a way to find this directory. tmux does not have a build-in command apparently nor sets an environment variable. I also skimmed over the man page, but didn't find anything in the COMMANDS or VARIABLES section. This directory needs to be saved somewhere though, as opening a new tmux window makes it go to this directory. Of course one I open a new window and close one everytime I want to achieve the desired behavior, but this is surely less than optimal and there needs to be a better way. Is there a way to achieve this behavior / get the session base directory in tmux? If so, how?