When I try to get a list of available services that can be used with
'systemctl status' by using tab completion I get "Failed to get D-Bus
connection: Connection refused" error message.

$ sudo systemctl status [TAB]Failed to get D-Bus connection: Connection refused

The error occurs also with other systemctl commands like start, stop or cancel.

This problem can be fixed by installing dbus package. Maybe having
dbus as a dependency for bash-completion would be a solution for this
problem?

My system information with 'uname -a':
Linux <hostname> 3.16.0-4-amd64 #1 SMP Debian 3.16.7-ckt20-1+deb8u1
(2015-12-14) x86_64 GNU/Linux

Also during the installation of this Debian Jessie system I deselected
everything from the menu where I was asked which software I wanted to
install.

I don't know how things like this are generally handled in Debian, but
would like to note that systemctl completion is not shipped by
bash-completion (at least upstream) so chances are that it should be
fixed somewhere else.

Oh, you're right, I just tested the autocompletion without
bash-completion installed and it still completed it. Should I make a
new bug report for systemd (or to some other pkg, if someone knows
which package specificly handles this completion?) or modify this bug
report somehow?