Previous answers are correct, but there’s another case where you could get that exception:
Making multiple requests without reading any intermediate responses completely.
For instance:
conn.request('PUT',...)
conn.request('GET',...)
# will not work: raises ResponseNotReady
conn.request('PUT',...)
r = conn.getresponse()
r.read() # <-- that's the important call!
conn.request('GET',...)
r = conn.getresponse()
r.read() # <-- same thing
and so on.