Large Language Models (LLMs) are increasingly used to generate summaries of software bug reports, including sections such as Steps-to-Reproduce (S2R), Actual Behavior (AB), and Expected Behavior (EB). However, these models frequently produce hallucinations that can be convincing but unsupported by the source report. This can mislead developers and reduce trust in automated maintenance tools. Existing hallucination detection approaches typically evaluate outputs at the full-response level and do not consider the structure of technical documents. An initial exploratory study on 80 structured bug report summaries found that approximately 47.9% contained missing information, while 12.3% included fabricated content, highlighting the need for systematic hallucination analysis in bug report summarization. In this work, we empirically investigate hallucinations in LLM-generated bug report summaries from a section-aware perspective. Using the BugsRepo dataset, derived from Mozilla OSS projects, we introduce controlled synthetic hallucination injection to construct a benchmark for training and evaluation. We propose a section-aware hallucination detection approach that jointly predicts whether a summary contains hallucinated content, identifies affected sections, and classifies hallucination types. Experimental results across multiple pretrained language models show that the proposed approach achieves strong performance across all tasks, with the best model obtaining 0.89 report-level Macro-F1, 0.83 section-level Macro-F1, and 0.84 hallucination-type Macro-F1. We further analyze common hallucination patterns and model failure modes to better understand limitations of current LLM-generated bug report summaries. The findings highlight the importance of section-aware hallucination analysis for improving the reliability of LLM-assisted bug report summarization in software maintenance workflows.