Here we initiate a systematic study of some of the symmetry properties of unimodular gravity, building on much of the known structure of general relativity, and utilizing the powerful technology developed in that context, such as the spinor helicity formal-ism. In particular, we show, up to five-points and tree-level, that the KLT relations of perturbative gravity hold for trace free or unimodular gravity. This work is in conjunction with a paper written with A. Welman, J. Murugan and G.F.R. Ellis (ARXIV: 1511.08517)