Yes, it is possible to import bank statement CSV files to Odoo automatically through the API or other methods. Odoo provides various ways to import data, including bank statement CSV files. Here are a few options you can explore:

1. Odoo Import functionality: Odoo has built-in import functionality that allows you to import CSV files. You can navigate to the respective bank statement model (e.g., account.bank.statement) and use the "Import" button to upload the CSV file manually. However, since you mentioned the need for an automatic process, this method might not be suitable for your requirement.

2. Odoo API: You can use the Odoo API to programmatically import the bank statement CSV files. You can write a custom script or develop an integration with the other app that sends the CSV files. The script or integration can utilize the Odoo API to create bank statement records based on the data from the CSV files. The account.bank.statement model and related models would be involved in this process.

3. Custom Module: You can develop a custom Odoo module that handles the automatic import of bank statement CSV files. Within the module, you can define a scheduled action or a cron job that periodically checks for new CSV files in a specific directory or receives them from the other app. The module can then parse the CSV files and create the corresponding bank statement records using Odoo's ORM (Object-Relational Mapping) functionalities.

By leveraging these options, you can automate the process of importing bank statement CSV files into Odoo, allowing for seamless integration with the other app and eliminating the need for manual file uploads. The best approach depends on your specific requirements, preferences, and the capabilities of the other app.