With the increasing utilization of large language models such as ChatGPT during software development, it has become crucial to verify the quality of code content it generates. Recent studies proposed utilizing ChatGPT as both a developer and tester for multi-agent collaborative software development. The multi-agent collaboration empowers ChatGPT to produce test reports for its generated code, enabling it to self-verify the code content and fix bugs based on these reports. However, these studies did not assess the effectiveness of the generated test reports in validating the code. Therefore, we conduct a comprehensive empirical investigation to evaluate ChatGPT's self-verification capability in code generation, code completion, and program repair. We request ChatGPT to (1) generate correct code and then self-verify its correctness; (2) complete code without vulnerabilities and then self-verify for the presence of vulnerabilities; and (3) repair buggy code and then self-verify whether the bugs are resolved. Our findings on two code generation datasets, one code completion dataset, and two program repair datasets reveal the following observations: (1) ChatGPT often erroneously predicts its generated incorrect code as correct. (2) The self-contradictory hallucinations in ChatGPT's behavior arise. (3) The self-verification capability of ChatGPT can be enhanced by asking the guiding question, which queries whether ChatGPT agrees with assertions about incorrectly generated or repaired code and vulnerabilities in completed code. (4) Using test reports generated by ChatGPT can identify more vulnerabilities in completed code, but the explanations for incorrectly generated code and failed repairs are mostly inaccurate in the test reports. Based on these findings, we provide implications for further research or development using ChatGPT.