You can if you give them names. For example, in your HTML:

<input type=submit name=do_connect value="Connect">
<input type=submit name=do_results value="Get Results">
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Then, in your program:

use CGI;
my $query = new CGI;
if ($query->param('do_connect')) {
    # connect to database
}
elsif ($query->param('do_results')) {
    # get results of sql call
}
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Or something along those lines.