You need to escape your backslashes and your dollar sign:

my $ref = `cmd.exe /c dir "\\\\swmn00xd00073\\D\$ | FIND /I "BYTES FRE
+E"`;
print "ref = $ref\n";
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The above worked for me, as shown below:

{C} > cat script.pl
#!/usr/bin/perl

use strict;

my $ref = `cmd.exe /c dir "\\\\192.168.78.129\\c\$" | find /i "bytes f
+ree"`;
print "ref = $ref\n";

{C} > script
ref =               14 Dir(s)   3,949,535,232 bytes free
[download]