Data uncertainty is ubiquitous in many real-world applications such as sensor/RFID data analysis. In this paper, we investigate uncertain data that exhibit local correlations, that is, each uncertain object is only locally correlated with a small subset of data, while being independent of others. We propose a generic framework for dealing with this kind of uncertain and locally correlated data, in which we investigate a classical spatial query, nearest neighbor query, on uncertain data with local correlations (namely LC-PNN). Most importantly, to enable fast LC-PNN query processing, we propose a novel filtering technique via offline pre-computations to reduce the query search space. We demonstrate through extensive experiments the efficiency and effectiveness of our approaches.