Strange, I don't see any obvious error related to the C "z" lib or to the Python "zlib" module.

Example on my system:

haypo@selma$ python3
Python 3.5.2 (default, Sep 14 2016, 11:28:32) 
[GCC 6.2.1 20160901 (Red Hat 6.2.1-1)] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import zlib
>>> zlib
<module 'zlib' from '/usr/lib64/python3.5/lib-dynload/zlib.cpython-35m-x86_64-linux-gnu.so'>
>>> 
haypo@selma$ ldd /usr/lib64/python3.5/lib-dynload/zlib.cpython-35m-x86_64-linux-gnu.so
	linux-vdso.so.1 (0x00007fff22f2e000)
	libz.so.1 => /lib64/libz.so.1 (0x00007f88e1fe0000)
	libpython3.5m.so.1.0 => /lib64/libpython3.5m.so.1.0 (0x00007f88e1b13000)
	libpthread.so.0 => /lib64/libpthread.so.0 (0x00007f88e18f5000)
	libc.so.6 => /lib64/libc.so.6 (0x00007f88e152f000)
	libdl.so.2 => /lib64/libdl.so.2 (0x00007f88e132b000)
	libutil.so.1 => /lib64/libutil.so.1 (0x00007f88e1126000)
	libm.so.6 => /lib64/libm.so.6 (0x00007f88e0e1d000)
	/lib64/ld-linux-x86-64.so.2 (0x000055d00b915000)
haypo@selma$ ldd /usr/lib64/python3.5/lib-dynload/zlib.cpython-35m-x86_64-linux-gnu.so^C
haypo@selma$ ls -l /lib64/libz.so.1
lrwxrwxrwx. 1 root root 13  5 févr.  2016 /lib64/libz.so.1 -> libz.so.1.2.8

Can you check if you have a "zlib.(...).so" file in /usr/lib64/python3.5/lib-dynload/? (ajust to the right directory)