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I was able to reproduce this error twice before it worked normally.

This is the backtrace that I could get.
I was unable to get the place in the source where the error is.

Thread 0 - System ID 3540
Entry point   php+2fb2 
Create time   4/5/2008 4:04:04 PM 
Time spent in user mode   0 Days 0:0:0.31 
Time spent in kernel mode   0 Days 0:0:0.93 

Function     Arg 1     Arg 2     Arg 3   Source 
php_mysqli!get_module+154b     00c0fb10     76299fab     01febdaa    
msvcrt!_getptd+8     01febdaa     00c0fb28     762add1d    
msvcrt!_LocaleUpdate::_LocaleUpdate+18     01fee9a0     01fee9d0     00000000    
php_mysqli!php_mysqli_set_error+5f17     00000001     01fee9d0     00000000    
php5ts!execute+a29     00000000     00000000     00000000    

PHP_MYSQLI!GET_MODULE+154BWARNING - DebugDiag was not able to locate debug symbols for php_mysqli.dll, so the information below may be incomplete.

In php__PID__3136__Date__04_05_2008__Time_04_04_24PM__490__Second_Chance_Exception_C0000005.dmp the assembly instruction at php_mysqli!get_module+154b in C:\Users\Joshua D. Washburn\Desktop\PHPMysql\PHP\php_mysqli.dll from The PHP Group has caused an access violation exception (0xC0000005) when trying to read from memory location 0x00000000 on thread 0

This is the test case:
--TEST--
Bug 44241: PHP Access Violation on Mysqli->fetch_array()
--FILE--
<?
/*
Database:
CREATE DATABASE alpha;
USE alpha;
CREATE TABLE beta (ID INT AUTO_INCREMENT UNIQUE KEY, Name TEXT);
INSERT INTO beta ("Name") VALUES ("Joshua");
INSERT INTO beta ("Name") VALUES ("Test");
INSERT INTO beta ("Name") VALUES ("Gamma");
INSERT INTO beta ("Name") VALUES ("Computer");
*/

$db = new mysqli("localhost","root");
$result = $db->query("SELECT * FROM alpha.beta");
while ($row = $result->fetch_array(MYSQLI_ASSOC))
{
	echo "[".$row["Name"]."]";
}
$result = $db->query("SELECT * FROM alpha.beta");
while ($row = $result->fetch_array(MYSQLI_NUM))
{
	echo "[".$row[1]."]";
}
$result = $db->query("SELECT * FROM alpha.beta");
while ($row = $result->fetch_array(MYSQLI_BOTH))
{
	echo "[".$row["Name"]."|".$row[1]."]";
}
?>
--EXPECT--
[Joshua][Test][Gamma][Computer][Joshua][Test][Gamma][Computer][Joshua|Joshua][Test|Test][Gamma|Gamma][Computer|Computer]
===DONE===

I can only reproduce the error if the libmysql.dll is replaced with a different version. Using the bundled version does not cause the problem.