Can I be held liable, for her mistake of not notifying the utility company to take the utilities out of her name?

I'm a new landlord and was very much taken advantage of by this tenant. TRUST ME I've learned a very very valuable lesson from this experience.

Short story: I own a duplex, live in one side and rent out the other.  My tenant that just moved out has been terrible!  
I’ve been very good to her, I let her move in 2-3weeks early rent free w/ the agreement that she painted the apartment.  Let her pay rent 2weeks late at a time, let her use my washer and dryer in my unit because she didn’t have one in her unit.  Allowed her to have two cats and a dog (that she never cleaned up after).  When her fridge broke she lost a bunch of food and I let her live there rent free until the fridge was fixed.  (1 week)

And I've done so many many nice supportive things for her throughout the duration of her lease.
She just moved out, did not patch any holes she drilled into the walls from curtains and pictures etc.  Did not do a deep clean leaving the apartment in move in ready condition. 
HOWEVER, she totally forgot to take the utilities out of her name and has now been paying for the electric and heat for this vacant unit for the past week.  

Can I be held liable, for her mistake of not notifying the utility company to take the utilities out of her name? 

First off welcome to being a landlord.  It isn’t as easy as people make it out to be. 

First you need to reset your brain to that of a business person and not someone’s friend.  You’ve given more to this tenant than I would give to most anyone I actually know. 

Second it’s not your responsibility to remove and turn off their utilities. You can’t be held liable for something that is out of your hands. 

Third, don’t ever let a tenant do any work inside the apartment ever.  And especially don’t trade rent for services it never works out in your favor.  

Lastly read a bunch of books and listen to podcasts that deal specifically with property management.  Get a iron clad lease so that all “what if’s” are laid out for both your protection and theirs.  

Good luck and just remember to learn from this and don’t repeat it. 

@Michael Hurley   I second what Eric said.  Your first mistake was letting her move in rent free so she could paint.  You need to be fair, but firm.  

Go through her unit, take lots of photos of the damage-include a ruler when taking photos of the holes in walls for scale.  Make a list of the damages and repair/cleaning costs and take that off her deposit.  Get a professional company in for the cleaning, so you have a bill to give her.

She is the one who forgot to take her name off the utilities.  That is HER problem.  Go ahead and put them in your name now, assuming the unit is vacant and leave it at that.  Don't mention it to her.

The real lesson: people will not appreciate your kindness.

Keeping the rent low, allowing changes to the lease, forgiving late payments, and giving Christmas gifts to your tenants is far more likely to hurt you than help you. Treat it like a business and your tenants will, too. Treat it like a friendship or demonstrate generosity and they will walk all over you.

Utilities are her responsibility. Once you discover the problem, you should do the right thing and convert them back into your name. The balance in her name is between her and the utility provider.

Many times I had tenants leave mid month and baile on me . Sadly  they are so lazy and suck at everything they do ,they often don’t practice their due diligence by removing their name from the utilities . I’ll just say this :I’m usually in no rush to call the utility companies up and switch it when this happens I can assure you lol