You are trying to find '\w+\-\$\.\%' pattern with (\w+\-\$\.\%) group and it does not exist so $1 is undefined and u get an error. Try this.

my $string="{'totalResultsCount':71-24,'securityList':[{'cusip':'91%27
+9-6.H:Y8','issueDate':'2016-06-02T00:00:00','securityType':'Bill'}";
# Patterns
# original (\w+\-\$\.\%)
# matach any pattern with these limits ([\w\-\$\.\%\:]+)
# anything but this ' ([^\']+)
# exact pattern (\d{2}\%\d{3}\-\d\.[A-Z]\:[A-Z]\d)
$string =~ /'cusip':'(\d{2}\%\d{3}\-\d\.[A-Z]\:[A-Z]\d)'/;
if (defined $1) {
print " first is : $1 \n\n";
}
else {
print " first is not defined\n\n";
}
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Updated: added some regex in code.