[c#] Should I call Close() or Dispose() for stream objects?

No, you shouldn't call those methods manually. At the end of the using block the Dispose() method is automatically called which will take care to free unmanaged resources (at least for standard .NET BCL classes such as streams, readers/writers, ...). So you could also write your code like this:

using (Stream responseStream = response.GetResponseStream())
    using (StreamReader reader = new StreamReader(responseStream))
        using (StreamWriter writer = new StreamWriter(filename))
        {
            int chunkSize = 1024;
            while (!reader.EndOfStream)
            {
                 char[] buffer = new char[chunkSize];
                 int count = reader.Read(buffer, 0, chunkSize);
                 if (count != 0)
                 {
                     writer.Write(buffer, 0, count);
                 }
            }
         }

The Close() method calls Dispose().

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