my ($fi, $fo) = ("/in.CSV", "/out.ins");
open my $hi, "<", $fi or die "$fi: $!\n";
open my $ho, ">", $fo or die "$fo: $!\n";
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just my 2cents... apart of the chomp-chop issue and the other things said, can't see the point on to create two extra variables here, why simply not do this?

open my $hi, "<", "/in.CSV" or die $!;
open my $ho, ">", "/out.ins" or die $!;
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You could also do something with this:

  if ($array[0] eq "\"Branchno\"") { next; }
    if ($array[0] eq "\"\"" ) {next;}
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You want to discard this lines?, then do it as early as you can, put both before the substitution lines. In a very big file this can make a difference.

While(<INST>) { 
 next if /^\"(Branchno|)\"/;
 s/...
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