Using statement in SQlite

Im trying to understand how to use a using statement in SQLite in order to avoids deadlocks and what not. Lets say I have this code in my repository:

 public SQliteRepository(SQLiteAsyncConnection connection)
    {
        _connection = connection;
        _connection.CreateTableAsync<User>();          
    }

    public async void SaveUser(User user)
    {           
        await _connection.InsertAsync(user);           
    }

I assume that I should wrap the SaveUser in a using-statement but the info I find usually deals with non-async code. Also, does this code mean that I open the connection in the CTOR and it stays open? Should I not assign the _connection at all in the CTOR?