Users have the utility called CHKLOG to periodically clear the event.log, but there is no utility to clear the connect.log file.  How is this done?

You can go ahead and delete the connect.log as it will create a new one for the next log entry. If you receive an error message when trying to delete it you will need to stop the server first. You can disable the creation of the connection log by deleting the "InstallDirectory" entry from the [SimbaServer] section of the odbc.ini file, which is located in the Relativity Data Server installation directory.