[AllenG (OP)]

What possible medical reason could cause this girl to cry tears?

A GIRL has become a holy shrine in India where worshippers watch her cry blood instead of tears.
Doctors in Patna, north-east India, have been stumped by Rashida Khatoon's condition, which causes her to shed tears of blood several times a day.

But local Hindu holy men have declared her a miracle.

And followers now flock to her home, showering her and her family with gifts as holy offerings.

Rashida said: "I do not feel any pain when it happens but it's a shock to see blood instead of water

Wait, I know--The Sun, but National Geographic is doing a show on her.

Hoax, or is there a medical cause?

[RD]

Possibly medical reason ...

Indian Journal of Ophthalmology
      
Year : 1987  |  Volume : 35  |  Issue : 1  |  Page : 41-43

Bloody tears (haemolacria)

BK Ahluwalia, AK Khurana, S Sood
 Department of Ophthalmology, Medical College Hospital, Rohtak 124 001, India

http://www.ijo.in/article.asp?issn=0301-4738;year=1987;volume=35;issue=1;spage=41;epage=43;aulast=Ahluwalia

or could be faked, (don't try this at home).

[Chemistry4me]

Me don't believe me eyes.

[Nizzle]

She had a bad plumber, connecting all the ducts in the wrong way.
She probably sweats urine, pees saliva and digests food with tears.

[that mad man]

I've seen a video of someone who can cry milk tears. He sucks up milk into his nose and can force it out of his tear ducts. If it can de done with milk then..

Wasn't it declared a Hindu miracle also when a statue was seen (allegedly) crying milk some time ago.

Not a bad way to get free gifts and offerings.