In recent years, code intelligence has gained increasing importance in the field of automated software engineering. Meanwhile, the widespread adoption of Pretrained Language Models (PLMs) and Large Language Models (LLMs) has raised concerns regarding data contamination and its potential impact on model performance evaluation. Previous studies mainly focused on sample-level contamination, ignoring partial contamination scenarios that are pervasive in code intelligence. This paper fills this gap and presents a systematic empirical study to investigate the fine-grained data contamination on mainstream code tasks. Our study involves diverse representative PLMs: RoBERTa and GPT-2, and LLMs: LLaMA and StarCoder, covering three major tasks: code translation, code generation, and code summarization, across two Programming Languages (PLs): Java and Python. We categorize contamination scenarios into four types according to the code intelligence practice, namely input-only, output-only, unpaired, and paired contamination settings, and construct corresponding experimental and control groups for exploration. Experimental results show that, under the pre-training, fine-tuning, and inference paradigm adopted by PLMs, even deliberately injecting paired contamination does not lead to significant performance overestimation. But direct inference or small-scale fine-tuning uncovers the contamination effects. In contrast, LLMs with pre-training and inference paradigm are significantly affected by the paired contamination. Apart from the above, other contamination scenarios have no impact on both PLMs and LLMs. Our findings challenge the conventional belief that contamination inevitably leads to performance overestimation, providing new insights into the evaluation and deployment of code intelligence models.