There isn’t a need to connect a ground wire as this is a connection that is needed between the turntable and it's phono preamp (whether the preamp is built into the turntable, or external).  When going from the very low level of a phono cartridge, it's easier to pick up noise when bringing this signal up to line level, and the ground wire helps with this.  On an internal preamp turntable, this connection is located inside the turntable. When going from the line level RCA out of a turntable with an internal phono preamp or the line level outputs from an external phono preamp to the inputs on your speakers, this connection is not needed.