You will not be arrested by the police.

Detailed explanation:

1. Overdue credit card debt will not lead to the direct arrest of an individual by the public security organs. Public security organs are mainly responsible for handling criminal crimes and public security cases, while credit card debts are civil debt issues.

2. Banks usually take some legal measures to recover arrears, such as through collection departments, lawyer letters, etc. However, these methods are limited to the civil field and do not involve public security organs.

3. If the debt continues to be overdue and the amount is large, the bank may file a lawsuit in court and seek judicial procedures to resolve the debt problem. Even so, it is the court that executes the judgment or ruling, rather than the direct involvement of the public security organs.

4. Credit card debt issues are usually handled by civil entities such as banks and courts, as well as relevant lawyers, and the legal procedures involved are mainly in the field of civil litigation.

Summary: Overdue payment of 40,000 yuan on a Bank of Communications credit card will not lead to arrest by the police. The bank will take legal measures to recover the debt, but this falls under the category of civil debt and has nothing to do with the public security organs.

Extended information: Credit card debt issues are civil debt disputes. According to China's "Contract Law" and other relevant legal provisions, banks can recover debts through collection departments, lawyer's letters, etc. If the amount owed is large, the bank may file a lawsuit with the court, and the court will make a legal judgment to recover the arrears. In this process, the public security organs will not directly intervene or arrest individuals unless criminal offenses are involved.