If you want your process to properly act as a daemon, then the simplest method is to use the Proc::Daemon module:

#!/usr/bin/perl -w
use strict;
use Proc::Daemon;
Proc::Daemon::Init;

# your code goes here

__END__
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This module takes care of all the little things necessary for proper daemonization: as per the docs:

1. Forks a child and exits the parent process.
2. Becomes a session leader (which detaches the program from the controlling terminal).
3. Forks another child process and exits first child. This prevents the potential of acquiring a controlling terminal.
4. Changes the current working directory to "/".
5. Clears the file creation mask.
6. Closes all open file descriptors.