I'm running CyanogenMod 13.0 without Play Services. I launched the Phone app and wanted to search through the contacts. Then a popup appeared, that:
Allow Phone to access this device's location?
What does a phone app need location for?
It might have something to do with Truecaller.
Some CyanogenMod isos integrate C-Apps directly into the OS, and Truecaller is a CallerID service with social media integration. Now, if you're not one for social media, I'd recommend blocking this off the bat. However, if you are, I'd recommend looking through the functionality further and determining whether it'd be useful for you or not.
But, then again, it might be something else. If you really want to be sure, I'd recommend going to the github page for your given CM distro and finding someone familiar with the code to take a look at the part that contains the phone application.