Multiple connection string in Web API 2

I have a Web API 2 using Dapper.net, and it's accessed by various client with their own database. Currently, I'm using custom header called Client-Id to identify the client.

This Client-Id contains a ConnectionString name and I passed this connection string into my constructor.

Here's my project structure:

Api.Persentation -> Api.Service -> Api.Logic

The connection string will pass from Api.Persentation to Api.Logic as follows:

Api.Persentation

public string testApi()
{
//using the service
//consider the connection string was handled on base class
var _myService = new testApiService(base.ConnectionString); 

return _myService.HelloWorld();
}

Api.Service

public class testApiService: BaseService
{
    #region const
    //This class was from API.Logic
    private readonly testApiRepo _testApiRepo;

    //the connectionString passed into base class to use a log repo
    public testApiService(string connectionString)
        : base(connectionString)
    {
        this._testApiRepo = new testApiRepo(connectionString);
    }
    #endregion


    public string HelloWorld()
    {
        //access API.Logic
        return this._testApiRepo.GetHelloWorld();
    }
}

Api.Logic

It has two classes, where BaseConnection is an abstract class to open the connection (the class how I use ConnectionString). The second one is, testApiRepo showing how I use the connection to get a database value.

/*-------------
BaseConnection Class
-------------*/
    public abstract class BaseConnection
    {
        private string _connectionString;
        public BaseConnection(string ConnectionString)
        {
            this._connectionString = ConnectionString;
        }

        public MyDbConnection GetOpenConnection(bool mars = false)
        {
            string cs = this._connectionString;
            if (mars)
            {
                SqlConnectionStringBuilder scsb = new SqlConnectionStringBuilder(cs);
                scsb.MultipleActiveResultSets = true;
                cs = scsb.ConnectionString;
            }

            //Finally we use the connection string in here
            var connection = new SqlConnection(ConfigurationManager.ConnectionStrings[this._connectionString].ToString());
            MyDbConnection DbConnection = new MyDbConnection(connection);
            DbConnection.Open();
            return DbConnection;
        }
    }

/*-------------
testApiRepo Class
-------------*/
    public class testApiRepo : BaseConnection
    {
        #region Const
        //the connection will handled on base class
        public CommissionRepo(string connectionString)
            : base(connectionString)
        {
        }
        #endregion

        public string GetHelloWorld()
        {
        //using base class to open connection
        using (var _db = base.GetOpenConnection())
        {
            string query = "SELECT 'HelloWorld'";
            var result = _db.Query<string>(query);
            return result.FirstOrDefault();
        }
    }
}