On Debian/Ubuntu you can do so using the dpkg search function:
# sudo dpkg -S /etc/init.d/whoopsie
whoopsie: /etc/init.d/whoopsie
On RedHat/CentOS you can use the rpm command:
# rpm -qf /usr/bin/bash
Tech tips, mostly to do with Linux, Ubuntu, Grails, PHP, development tools and so on...
# sudo dpkg -S /etc/init.d/whoopsie
whoopsie: /etc/init.d/whoopsie
# rpm -qf /usr/bin/bash
$ dpkg-query -L vsftpd
/.
/usr
/usr/share
/usr/share/doc
/usr/share/doc/vsftpd
/usr/share/doc/vsftpd/FAQ.gz
/usr/share/doc/vsftpd/examples
...
...
/usr/share/doc/vsftpd/changelog.Debian.gz
/usr/share/doc/vsftpd/REWARD
/usr/share/doc/vsftpd/SPEED
/usr/share/man
/usr/share/man/man8
/usr/share/man/man8/vsftpd.8.gz
/usr/share/man/man5
/usr/share/man/man5/vsftpd.conf.5.gz
/usr/sbin
/usr/sbin/vsftpd
/etc
/etc/init.d
/etc/pam.d
/etc/pam.d/vsftpd
/etc/init
/etc/init/vsftpd.conf
/etc/vsftpd.conf
/etc/logrotate.d
/etc/logrotate.d/vsftpd
/etc/ftpusers
/etc/init.d/vsftpd
# rpm -ql yum-cron
/etc/cron.daily/0yum.cron
/etc/rc.d/init.d/yum-cron
/etc/sysconfig/yum-cron
/etc/yum/yum-daily.yum
/etc/yum/yum-weekly.yum
/usr/share/doc/yum-cron-3.2.29
/usr/share/doc/yum-cron-3.2.29/COPYING