Final tests on the gelato at the centre of the Coogee Bay Hotel scandal have come back inconclusive, with the DNA trace too weak to identify the person responsible for the murky affair.

The NSW Food Authority has declared "case closed" after completing testing on a sample of gelato served to the Whyte family at the hotel on October 5, and which was found to contain faeces.

The Sydney family were served the free ice-cream after earlier complaining about the hotel's service.