How many days do you usually report to the local authorities after receiving the notice of criminal proceedings from China Merchants Bank?

There is no so-called "notice of criminal proceedings" in law. I don't know exactly what you received. If it is not a fraudulent phone call, if you owe a bank loan or credit card, the bank may send a lawyer's letter to collect it. If the repayment is still not made after collection, a civil lawsuit may be filed or credit card fraud may be reported to the judicial organ as appropriate.

According to the provisions of Article 175th of the Procedure for Handling Criminal Cases by Public Security Organs:

1. After accepting a case, the public security organ considers that the criminal facts that need to be investigated for criminal responsibility belong to its own jurisdiction, and shall file a case with the approval of the person in charge of the public security organ at or above the county level.

2. If it is considered that there is no criminal fact, or the criminal fact is obviously minor and does not need to be investigated for criminal responsibility, or there are other circumstances in which criminal responsibility is not investigated according to law, the case shall not be filed with the approval of the person in charge of the public security organ at or above the county level.