Automatic Speech Recognition (ASR) systems are widely deployed across linguistically diverse regions, yet their ability to generalize across fine-grained geographic variation remains underexplored. We present a systematic study of cross-district ASR generalization for Indian languages, analyzing the impact of regional variation on performance. Using finetuning as a controlled probe, we train models on speech from a single district and evaluate them on other districts within the same language. We examine trends across multiple train test district pairs and quantify performance differences. To assess geographic effects, we analyze the correlation between WER and inter district distance using two distance measures. Our results show consistent correlations between geographic distance and WER, highlighting the challenges of regional generalization and the need for geographically diverse speech data in ASR development and evaluation in India.