The following works for me:

my $string = '\\\\domca-prn01\DH4-2139-HP4';
if ( $string =~ /\\\\.*\\.*/) {
        print"match\n";
}
[download]

Note that I had to double the backslashes in the string, because the first one was escaping the second. You also probably want to use a character class (e.g., [\w-]+) or at least [^\\]+ instead of .*.