"Inspections (.NET) runner" in TeamCity is the same thing as "ReSharper CommandLine Tools" is. So, I guess, "Introducing InspectCode" article will help you to adjust needed settings.
Well, if you want to configure InspectCode on a TeamCity server, you can make all configurations locally with ReSharper, save the settings to the Solution Team-Shared layer, and then commit the resulting {SolutonName}.sln.DotSettings file (this file is stored in the root directory of the solution near .sln file) in your VCS. InspectCode on the server will find and apply these settings.
As an alternative, you can configure InspectCode by specifying a shared .DotSettings file through the /profile (/p) parameter.