Duplicate Check offers a REST API which can be used to search record in Salesforce or insert/update records in Salesforce via the Data API.
The REST Data API allows for the creation of record without the need of creating duplicates. When a record is added via the Data API this record is directly checked for duplicates. If duplicates are present it will update the existing record instead of creating a duplicate record.
The API documentation can be found via swaggerhub.
You need to authenticate yourself before you can use the REST Api. The authentication works via the standard Salesforce Rest Authentication methods. You can read more about this via the REST API Developer Guide.