I recommend you clearly separate the parsing of the input from the formatting and outputting of the CSV records. This is a more maintainable and less error-prone technique than inputting/parsing and formatting/outputting simultaneously. I also think using modular arithmetic with $. ($INPUT_LINE_NUMBER) is less clear than simply reading each trio of lines explicitly as AppleFritter demonstrated here.

I also recommend you use autodie, explicitly specify the character encodings of the two text files, and explicitly close both file handles.

use autodie qw( open close );

my $input_file  = 'clients.txt';
my $output_file = 'clients.csv';

open my $input_fh,  '<encoding(UTF-8)', $input_file;
open my $output_fh, '>encoding(UTF-8)', $output_file;

# Process the client data file...

close $input_fh;
close $output_fh;

exit 0;
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