Wow, I hope you never have a complaint to report to the Complaint Department! Word to the wise: the Complaint Department doesn't exist. You will be arrested.
I'm pretty sure most western countries have a complaints department for law enforcement.
Many years ago in my teenage years in New Zealand, I was chatting to random people on IRC (a pretty new protocol at the time) and there was a guy bragging about bombing a plane - specifically, putting explosives on the landing gear of the plane.
Being young and paranoid, but not yet particularly clever in the ways of the computer security world, I 'anonymously' emailed the police with information about it. My attempts at anonymity were however not good enough and a few days later the police came and took all my computer equipment. The search warrant read "Attempted murder and breach of the telecommunications act" (I still have it, along with the write up I got in the newspaper as a reminder of absurdity). Of course, I was never arrested as I had done nothing illegal.
While that all annoyed me greatly, it didn't annoy me nearly as much as them keeping my stuff for over 3 months before I got it back. When I did finally get it back, the power switch on my main system was physically broken and the HDD was formatted.
I made a complaint to the Police Complaints Authority (a government body) and they ended up writing a letter of apology. So, while complaining certainly didn't do anything useful for me, the point is that there WAS a body for me to complain to.
I'm sure it's a little more complex in countries like the US and Australia since there may be differences by state as well as the federal level to think about, but a quick Google search seems to confirm that complaints departments and/or processes do exist there also.