The original question concerned the first letter of $title, whereas your answer compares the first character.

To match the first letter case insensitively, try:

my $title="$dbrow{'Title'}";

$title =~ m/([a-z])/i;    # Match the first letter in $title
if (lc($1) eq lc($layer)) {
    #do something...
}
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NB. I'm using [a-z] rather than \w because \w includes the underscore character, which isn't a letter.

Given that you seem to be working with results returned from a database, it's almost certainly better to check the first letter matches in the SQL query, rather than in the Perl code later on. Try something like SELECT * FROM table WHERE field LIKE "A%" to match records where field starts with the letter A.