I completely like this game, finished it years ago. But this version dissapointed me. First, why music in the game is very loud, and changing the volume settings doesn't help at all. As I see in the .ogg file it's for sure high quality, but listening it without hearing what's going around is not neat.
Even putting volume down is not disabling music...
I think it's because the game uses other audio wrapper to play .ogg file and it's not affilated to the game settings.
This indeed should be fixed.

I just deleted all files from Crime Cities\Music

It's not an elegant solution, but one possibility would be to run the .ogg file through an audio editing program (Audacity is one that is free and easy to use), lower the volume and replace the music with that version.

I'm adding another potential way to solve this, with DxWnd - which doesn't work for me right now, still it may work for others and it will surely change given this wrapper is very regularly updated, so it's worth keeping an eye on this.

Open the game directory and rename/move 'winmm.dll' elsewhere.

Download DxWnd on Sourceforge, launch it as Admin and add the game executable (right-click in the tool UI, Add).

In the 'options' menu, check that 'Expert mode' is enabled.

Right-click on the game newly created icon and choose Modify.

From there go into the Sound tab and check 'Set Emulated CD Volume' (setting the slider to a desired value), and 'Virtual CD Audio'.

Then use the 'Try' button to check if it's working (I can hear the main menu music but not the in-game track, I guess it's because the main menu is just a music file instead of a CD-audio track).

Then click OK and exit the tool (it will ask you to save).

Note that with the default settings, it will probably run the game windowed (which can be useful if you want to adjust the music volume when relying on a plain music player!). To prevent this, untick 'Run in window' on the 'Main' tab.

You can then launch the game through DxWnd, or let it run in the background as it will 'hook' the game process when launching it from the usual shortcut (if it doesn't, check the Hook setting in 'File').

Is there any way to turn down the music in game? When I turn the music down in the options menu the music volume doesn't change at all.

I did that today. I came here to see if the GoG version has the same problem as the steamed one. I made a quieter version of the file and I also mixed my own soundtrack of Gary Numan, Skinny Puppy, The Eurythmics, The Art Of Noise, and The Church, and Men Without Hats. It synchronizes well with the realtime gameplay demo, and the quiet version seems to be at a decent level. I'm uploading the mix tape in loud and quiet format on The Archive. I won't be uploading the muted O.S.T.

https://archive.org/details/track-02-new/Track02-new-quiet.ogg

The composer seems to have released the soundtrack on Bandcamp. I'm not sure they're the same. I think the Bandcamp version is maybe just rendered fancier/re-mixed.
https://pawelblaszczak.bandcamp.com/album/crime-cities-original-game-soundtrack