Controversy exists around owned dogs’ impacts in public open spaces, with concerns about dogs’ impact on wildlife, including birds. Leashing dogs in public open spaces offers a tractable way of reducing dogs’ deleterious impacts on birds. Although dogs in public spaces are often unleashed, some dogs roam freely, whilst other unleashed dogs remain close to their owners. It is currently unknown whether birds can perceive and incorporate subtle differences in the leash status of approaching, but non-roaming, dogs into their escape decisions. We compare escape responses of a common urban bird, the magpie-lark Grallina cyanoleuca, in parks in Melbourne, Australia, to standardized approaches by a walker and a dog, which was either leashed or not leashed (but with the dog at the same distance from the walker). Flight-initiation distances, the distance between the lark and dog when escape commenced, did not vary between treatments. However, the unleashed dog evoked more intense responses (mostly flying away) than the leashed dog (mostly walking away). Thus, this species appears to perceive unleashed dogs as especially threatening, independent of their roaming behavior. Our findings suggest that leashing may be an effective way to reduce dog disturbance to wildlife, even for non-roaming dogs.