Hi,
I have a similar issue with my dad's iphone 5s......i did an OTA update to 9.0.1 to it and after successful installation, the phone app just freezes....i'm not able to switch between the dialer to contacts or any tab in the phone app....even when i try to go to settings>phone, it just freezes after clicking on it....rest all app settings or iphone settings seem to work...
I tried a soft reboot by holding the home button and power button together, which infact made the phone app work for a few seconds i.e. i was able to switch between tabs but within 5-10 seconds, it froze again.....
Its is really frustrating to see that ios 9.0.1 still have so many issues which obviously apple hasn't looked into....
I'm gonna try and go back to 8.4.1 to check whether it works or not!!!!
Any help would be appreciated!!!!!