I am a U.S. citizen working on my application for permanent residency
in Canada. I have explored all of the websites and made a call to the
Buffalo consulate but do not have a definitive answer to this
question:
 The Canadian "Citizen and Immigration Canada" website indicates that
a police certificate is neccessary and should be submitted with the
application.  The Buffalo Consulate, however, states that if one is
coming from the U.S. - one should only provide a police certificate if
specifically asked to do so.....
I want to reduce the chance of delays.  Is is neccessary to provide
the certificate or not?

Hi there! 
Yes, get an police certificate. You will need to get one eventually
regardless. it is best to get it now rather than later. I immigrated
from Canada to the USA so I have been through what you are going
through. The certificate will prove to the Canadian immigration
officers that you do not hav ea criminal background and will make your
paper work go faster and smoother. Goodluck!!!