A birthday attack tries to find collisions on cryptographic hash functions. crc32 is not cryptographic, but it is a hash function.

The following code finds collisions easily:

<?php
$cache = [];

// 50% chance of collision after 2^16 tries

foreach(range(1, 2**16) as $foo) {
    $n = rand();
    $hashsum = crc32($n);

    if (isset($cache[$hashsum])) {
        print "Collision: crc32($n) == crc32({$cache[$hashsum]}) == $hashsum\n";
    } else {
        $cache[$hashsum] = $n;
    }
}

The crc32 hashsum is 32 bits in length. After 2^16 tries there is a 50% chance of finding a collision.