Does a Center-Tapped RF Balun Perform Better than Untapped Baluns?
For RF transformers/baluns, the inter-winding capacitance can play a big part in reducing common-mode signals between unbalanced input and balanced output. A 1 pF inter-winding capacitance may not seem that much but, at 1 GHz, it's an impedance of 159 ohms.

So, if you don't ground the centre-tap your balun won't be working as effectively as it can do because the balanced output will be strongly capacitively coupled to the unbalanced input. For most circuits this won't matter, but if you are relying on very low common-mode coupling then you need to ground the centre-tap.