dmmiller2k is right.
You also want to be sure that the 'text' that you are reading is examined as a single string, by your matching pattern (not one line at a time).
Then the regex is pretty simple (but note the /s operator is added, as dmmiller2k advised).

#!/usr/bin/perl -w

use strict;

#examine DATA as a single string.
$/ = '';
while (<DATA>){

#'.' will match \n with the /s operator
  if ( m/if.+else/s ){
     s/{//;
     s/}//;
  }

  print;
}

__END__
if (c=e)
{                  #// delete this curly brace
    call pgme;
    call pgmd;
}           
else
{ 
    call pgmd;     #// keep these curly braces
    call pgmc; 
}


if (c=e)
{                  #// delete this curly brace
    call pgme;
    call pgmd;
}           
else
{ 
    call pgmd;     #// keep these curly braces
    call pgmc; 
}
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mkmcconn
update please note that this regex example is
for illustration only - it's easily broken and the reason
it appears to work is because of the structure of the data
example.