Try:
sudo chsh -s /bin/zsh
Your entered password will not echo to the screen. If you have already successfully changed the shell, then yes, it would tell you no changes were made.
Now, you will need a new Zsh shell dot file to establish your PATH and Terminal prompt as the Zsh shell does not read the old Bash dot files. If you do not have a /Users/username/.zshrc file, then copy/paste the following into the launched Terminal followed by a return:
<<"EOF" > ~/.zshrc
export PATH=".:/usr/local/bin:${PATH}"
PS1="%m: %~ %% "
EOF
Once you have done that, then do the following at the Terminal prompt:
source ~/.zshrc
and now your PATH and Zsh shell prompt are set in the current Terminal session and for any subsequent launch of the Terminal.