Unmanned Aerial Vehicles (UAVs) have recently attracted significant attention due to their outstanding ability to be used in different sectors and serve in difficult and dangerous areas. Moreover, the advancements in computer vision and artificial intelligence have increased the use of UAVs in various applications and solutions, such as forest fires detection and borders monitoring. However, using deep neural networks (DNNs) with UAVs introduces several challenges of processing deeper networks and complex models, which restricts their on-board computation. In this work, we present a strategy aiming at distributing inference requests to a swarm of resource-constrained UAVs that classifies captured images on-board and finds the minimum decision-making latency. We formulate the model as an optimization problem that minimizes the latency between acquiring images and making the final decisions. The formulated optimization solution is an NP-hard problem. Hence it is not adequate for online resource allocation. Therefore, we introduce an online heuristic solution, namely DistInference, to find the layers placement strategy that gives the best latency among the available UAVs. The proposed approach is general enough to be used for different low decision-latency applications as well as for all CNN types organized into the pipeline of layers (e.g., VGG) or based on residual blocks (e.g., ResNet).