Q:

Command to list assigned dhcp addresses

Is there a command I can use to ask the dhcpd server which addresses have been assigned? 

A:

isc-dhcpd package version 4.3.1 has this command to list leases:
dhcp-lease-list --lease PATH_TO_LEASE_FILE

This is a simple perl script script that also supports older DHCP releases. You can see a copy in the Debian source code or in the official DHCP distribution (in contrib/) as well.
The output is pretty:
$ perl contrib/dhcp-lease-list.pl --lease /var/db/dhcpd/dhcpd.leases
To get manufacturer names please download http://standards.ieee.org/regauth/oui/oui.txt to /usr/local/etc/oui.txt
MAC                IP              hostname       valid until         manufacturer
===============================================================================================
90:27:e4:f9:9d:d7  192.168.0.182   iMac-de-mac    2015-12-12 01:37:06 -NA-
d8:a2:5e:94:40:81  192.168.0.178   foo-2          2015-12-12 01:04:56 -NA-
e8:9a:8f:6e:0f:60  192.168.0.127   angela         2015-12-11 23:55:32 -NA-
ec:55:f9:c5:f2:55  192.168.0.179   angela         2015-12-11 23:54:56 -NA-
f0:4f:7c:3f:9e:dc  192.168.0.183   kindle-1234567 2015-12-11 23:54:31 -NA-
f4:ec:38:e2:f9:67  192.168.0.185   -NA-           2015-12-11 23:55:40 -NA-
f8:d1:11:b7:5a:62  192.168.0.184   -NA-           2015-12-11 23:57:34 -NA-

It's prettier if you download the oui.txt file as suggested, but then the output can get garbled unless you apply the following patch:
--- dhcp-lease-list.pl.orig     2015-12-12 12:30:00.000000000 -0500
+++ dhcp-lease-list.pl  2015-12-12 12:54:31.000000000 -0500
@@ -41,7 +41,7 @@
     if (defined $oui) {
        $manu = join('-', ($_[0] =~ /^(..):(..):(..):/));
        $manu = `grep -i '$manu' $oui | cut -f3`;
-       chomp($manu);
+       $manu =~ s/^\s+|\s+$//g;
     }

     return $manu;
@@ -142,7 +142,7 @@
     }
     foreach (@leases) {
        if ($opt_format eq 'human') {
-          printf("%-19s%-16s%-15s%-20s%-20s\n",
+          printf("%-19s%-16s%-14.14s %-20s%-20s\n",
                  $_->{'mac'},       # MAC
                  $_->{'ip'},        # IP address
                  $_->{'hostname'},  # hostname

This patch was submitted upstream as ISC-Bugs #41288 and awaits review.

A:

No, you can only get this information server side from the DHCP server. This information is contained in the DHCP server's .lease file: /var/lib/dhcpd/dhcpd.leases, if you're using ISC's DHCP server.
Example
$ more /var/lib/dhcpd/dhcpd.leases
# All times in this file are in UTC (GMT), not your local timezone.   This is
# not a bug, so please don't ask about it.   There is no portable way to
# store leases in the local timezone, so please don't request this as a
# feature.   If this is inconvenient or confusing to you, we sincerely
# apologize.   Seriously, though - don't ask.
# The format of this file is documented in the dhcpd.leases(5) manual page.
# This lease file was written by isc-dhcp-V3.0.5-RedHat

lease 192.168.1.100 {
  starts 4 2011/09/22 20:27:28;
  ends 1 2011/09/26 20:27:28;
  tstp 1 2011/09/26 20:27:28;
  binding state free;
  hardware ethernet 00:1b:77:93:a1:69;
  uid "\001\000\033w\223\241i";
}
...
...

A:

egrep command can be used to get an output:
egrep "lease|hostname|hardware|\}" /var/lib/dhcpd/dhcpd.leases

Output:
lease 192.168.11.10 {
  hardware ethernet 20:6a:8a:55:19:0a;
  client-hostname "Maryam-PC";
}
lease 192.168.11.7 {
  hardware ethernet 00:16:ea:51:d3:12;
  client-hostname "parsoon";
}
lease 192.168.11.3 {
  hardware ethernet 00:17:c4:3f:84:e3;
  client-hostname "zahra-ubuntu";
}
lease 192.168.11.5 {
  hardware ethernet 58:b0:35:f1:31:2f;
}

