There are different ways to deal with this:
i. In case of fewer resources to be connected, a local database can be connected to such an application using the Azure VNET-based point-to-site service.
ii. Site-to-site or express routes are the solutions if more resources need to be connected. Due to the VPN's reliance on public infrastructures, such as the internet, response time may get delayed from site to site. Alternatively, express routes can be used in this scenario because they have a dedicated leased line that overcomes lag constraints.
iii. In case none of the above options are suitable, a Windows Communication Foundation (WCF) service can be built and hosted locally. The CRUD operations in the service would remain specific to the local database.