StreamReader and seeking

can you use streamreader to read a normal textfile and then in the middle of reading close the streamreader after saving the current position and then open streamreader again and start reading from that poision ?

if not what else can i use to accomplish the same case without locking the file ?

something like this:

 var fs = File.Open(@"C:\testfile.txt", FileMode.Open, FileAccess.Read);
        var sr = new StreamReader(fs);
        Debug.WriteLine(sr.ReadLine());//Prints:firstline
        var pos = fs.Position;
        while (!sr.EndOfStream)
        {
            Debug.WriteLine(sr.ReadLine());
        }
        fs.Seek(pos, SeekOrigin.Begin);
        Debug.WriteLine(sr.ReadLine());//Prints Nothing, i expect it to print SecondLine.

@lasseespeholt

here is the code i tried

            var position = -1;
        StreamReaderSE sr = new StreamReaderSE(@"c:\testfile.txt");
        Debug.WriteLine(sr.ReadLine());
        position = sr.BytesRead;
        Debug.WriteLine(sr.ReadLine());
        Debug.WriteLine(sr.ReadLine());
        Debug.WriteLine(sr.ReadLine());
        Debug.WriteLine(sr.ReadLine());
        Debug.WriteLine("Wait");
        sr.BaseStream.Seek(position, SeekOrigin.Begin);
        Debug.WriteLine(sr.ReadLine());