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...