The conservation of large carnivores in human-dominated landscapes needs to be reconciled with the safety of humans and domestic animals. This is especially true for the leopard Panthera pardus, which occurs extensively in agricultural landscapes and remnant forest tracts embedded within peri-urban areas such as Kathmandu district in Nepal. We carried out interviews in 321 households in this district to determine the extent of leopard habitat use and predation on domestic animals (dogs and goats) during October 2015–April 2016. We used multi-state occupancy models, and estimated probabilities of leopard habitat use (Ψ1) and predation on domestic animals (Ψ2) as a function of covariates, while accounting for imperfect detection. Our findings indicate that the rapidly urbanizing outskirts of Kathmandu city are used extensively by leopards. The estimated probability of fine-scale habitat use in 2 km2 sample units was 0.96 ± SE 0.05 and the probability of predation on domestic animals was 0.76 ± SE 0.15. Leopard attacks occurred in areas with high vegetation cover and abundant goats. Addressing the problem of leopard attacks on domestic animals will require developing a comprehensive mitigation plan that includes educational activities to raise awareness, measures to address grievances of affected local communities, interventions to prevent attacks on livestock, compensation programmes, and rapid response teams to ensure human and animal welfare in conflict-prone areas. Land-use planning in these peri-urban landscapes needs to facilitate the safe sharing of space between people and leopards.