We investigate the relation between star formation rates and local galaxy environment for a stellar mass selected galaxy sample in the redshift range 1.5 < z < 3. We use near-infra-red imaging from an extremely deep Hubble Space Telescope survey, the GOODS-NICMOS Survey (GNS) to measure local galaxy densities based on the nearest neighbour approach, while star-formation rates are estimated from rest-frame UV-fluxes. Due to our imaging depth we can examine galaxies down to a colour-independent stellar mass completeness limit of log Mast = 9.5 Modot at z ~ 3. We find a strong dependence of star formation activity on galaxy stellar mass over the whole redshift range, which does not depend on local environment. The average star formation rates are largely independent of local environment apart from in the highest relative over-densities. Galaxies in over-densities of a factor of > 5 have on average lower star formation rates by a factor of 2 - 3, but only up to redshifts of z ~ 2. We do not see any evidence for AGN activity influencing these relations. We also investigate the influence of the very local environment on star-formation activity by counting neighbours within 30 kpc radius. This shows that galaxies with two or more close neighbours have on average significantly lower star formation rates as well as lower specific star formation rates up to z ~ 2.5. We suggest that this might be due to star formation quenching induced by galaxy merging processes.