That's more complex that it sounds: a "blank line" could be this:
1,2,3
4,5,6
Which is trivial to remove:
File.WriteAllLines(fileName,File.ReadAllLines(fileName).Where(l => !string.IsNullOrWhiteSpace(l)));
Or it could refer to this:
1,2,3
,,,
4,5,6
Which is a lot harder - it requires "proper" parsing, because it could be
"1","2","3"
"","",""
"4","5","6"
In this case, you really want to look at the structures that you are reading this into, and remove empty instances of that directly before writing the CSV file.
And we can't help you with that: we have no idea how your software works!