Previous research has found that Acoustic Models (AM) of an Automatic Speech Recognition (ASR) system are susceptible to dialect variations within a language, thereby adversely affecting the ASR. To counter this, researchers have proposed to build a dialect-specific AM while keeping the Language Model (LM) constant for all the dialects. This study explores the effect of dialect mismatched LM by considering three different Telugu regional dialects: Telangana, Coastal Andhra, and Rayalaseema. We show that dialect variations that surface in the form of a different lexicon, grammar, and occasionally semantics can significantly degrade the performance of the LM under mismatched conditions. Therefore, this degradation has an adverse effect on the ASR even when dialect-specific AM is used. We show a degradation of up to 13.13 perplexity points when LM is used under mismatched conditions. Furthermore, we show a degradation of over 9% and over 15% in Character Error Rate (CER) and Word Error Rate (WER), respectively, in the ASR systems when using mismatched LMs over matched LMs.