What is required to deny a debit card dispute? Our customer came in to dispute several debit card transactions. On the dispute form she just checked that she did not conduct the transactions. We believe she is lying. Her story keeps changing going from home invasion to just a simple claim that "I did not conduct those transactions." We asked for a copy of the police report for the home invasion and it was not reported. We are trying to get photos for the ATM transactions, but that takes time. Thanks in advance for the advice.

There is no black and white answer to your question. On the one hand there is Reg E which simply requires that the customer enter a claim and the bank investigate. Under Reg E you are forbidden from requiring a police report, although you may ask for one. Also you cannot deny a transaction simply because a PIN was used.
On the flip side, this is not a court of law and you are not required to have "indisputatable proof" Reg E only requires that you investigate. You are permitted to use patterns of account history and usage in making your determination. For example, if a customer always makes cash withdrawals at an ATM at Main St. & Broadway around the same time every week, and then mysteriously disputes a month's worth, you may point to account history.
Also don't forget VISA/MC Zero Liability coverage may apply to non-PIN based purchases, depending on the circumstances.

Some questions to ask
#1. Did you loan your card to someone who exceeded your authority to use the card?
#2. If the card was loaned, did you get it back?
#3. If the card was in fact stolen, is there anyone else in the house who may have had access to it who also would have known the PIN?

If someone abused their privledge to use the card, then you may deny the claim. If she got the card back, and the same individual later stole it, she has a valid claim under Reg E, but make sure she knows the bank will file a police report against the individual. If she sticks to her story that no one had access to the card, no one knew the PIN, and she has no idea what happenned, you're back to working off the account history and trying to get video.

Update - we have a copy of the video clearly showing the customer using the ATM and getting funds that she states she did not do. This contradicts what she has reported to the police. Should we inform the the police that she may a filed a false police report?

I would.

i certainly would notify them, attempted fraud at a minimum, and depending on the amount taken could be more sever charges

Unless she could give me a very good reason for the memory lapse, I would likely close the account. I might also consider filing a SAR, regardless of whether the threshhold is triggered, to ensure it can be picked up by law enforcement if she is playing this game with multiple banks.

Police are pursuing the case. They have a copy of the video and plan on getting warrants. Apparently, filing a falst police report is a misdemeanor. The police have another crime, false writing on a report or smoething like that, they intend to charge them with. That crime is a felony. Account will be closed. Total amount disputed is less than $500. We were encouraged by the police to file our own police report claiming attempted theft by deception. Police say customer has a record.

Attaboy! Glad to see some action. The bank will only have expenses in this relationship now, but penalizing the person is the right thing to do. Certainly they should have no card and I'd say no account at this point.

Sometimes the good guys win!