The four died apparently after consuming poison while plastic covers were found wrapped on their faces at their 5th floor apartment in the 15-storeyed Odyessey building in Bhakti Park area of Wadala.
The victims were identified - Donato Anthony, his wife Lizey and two children Jason and Babit, police said.
Preliminary probe suggests it could be a case of suicide, they said.
The hands of Anthony were tied, police said, adding that they were also probing the murder angle.
The family was staying on rent in the flat, police added.