A minimal init script
It's clear, nicely formatted, and passes http://www.shellcheck.net/# with flying colors. I have only minor nitpicks.

The variable name command_line is too generic.
If you make it more descriptive,
for example start_command,
then the purpose of the pgrep line becomes easier to understand:
it should match whatever was used to start the command.

This maybe a matter of taste, but I like to place the ;; in case statements at the same indent level as the body of the statement, for example:

case "$1" in
    start)
        start
        ;;       # aligned with the commands, not the label
    stop)


I'm not really aware of a standard, but for what it's worth,
Vim's auto-indent function (and auto-reindent with gg=G) indents this way.
This writing style is also practical when folding is enabled in Vim,
making long case statement blocks appear like this:

case "$1" in
    start)
        --- # folded lines
    stop)
        --- # folded lines
    restart|force-reload)
        --- # folded lines


Well, this is really a nitpick, and a matter of taste, 
your way is perfectly fine too.