In humans, there is evidence that sensory processing of novel or threatening stimuli is right hemisphere dominated, especially in people experiencing negative affective states. There is also evidence for similar lateralization in a number of non-human animal species. Here we investigate whether this is also the case in domestic cattle that may experience long-term negative states due to commonly occurring conditions such as lameness. Health and welfare implications associated with pain in lame cows are a major concern in dairy farming. Behavioural tests combining animal behaviour and cognition could make a meaningful contribution to our understanding of disease-related changes in sensory processing in animals, and consequently enhance their welfare. We presented 216 lactating Holstein-Friesian cows with three different unfamiliar objects which were placed either bilaterally (e.g. two yellow party balloons, two black/white checkerboards) or hung centrally (a Kong™) within a familiar area. Cows were individually exposed to the objects on three consecutive days, and their viewing preference/eye use, exploration behaviour/nostril use, and stop position during approach was assessed. Mobility (lameness) was repeatedly scored during the testing period. Overall, a bias to view the right rather than the left object was found at initial presentation of the bilateral objects. More cows also explored the right object rather than the left object with their nose. There was a trend for cows appearing hesitant in approaching the objects by stopping at a distance to them, to then explore the left object rather than the right. In contrast, cows that approached the objects directly had a greater tendency to contact the right object. No significant preference in right or left eye/nostril use was found when cows explored the centrally-located object. We found no relationship between lameness and lateralized behaviour. Nevertheless, observed trends suggesting that lateralized behaviour in response to bilaterally located unfamiliar objects may reflect an immediate affective response are discussed. Further study is needed to understand the impact of long-term affective states on hemispheric dominance and lateralized behaviour.