I'm an accidental landlord - we lived in a 1-bed flat and when I got pregnant with my first we obviously needed somewhere bigger. If I sold I'd be in negative equity so I rented the flat out and we rented elsewhere.
I've had a few tenants in over the 4 years and had a lady in before my current tenant. She was looking for a temporary home as she'd sold her house and hadn't found another house to live in yet. So we agreed to a 6 month contract with 1 month rolling thereafter.
I knew when she first moved in that she was overlapping on moving out her old home by about a week so she could clean, get things in storage etc. However there were delays on her chain so she didn't actually occupy the flat until 3 weeks after her tenancy start date.
She was an OK tenant. Only problems I had was she'd complain about non-issues or issues I could do nothing about (like slugs coming into the garden) and she also painted the kitchen without permission then tried to charge me £35 for the cost of paint (I refused).
She found a house to buy quicker than expected and because it was empty she was able to exchange and move in very quickly. As a result she asked if she could end the tenancy 3 months early with 5 days notice. TBH it wasn't ideal for me, I like to have 4 weeks notice stipulated in the contract to find a new tenant, get paperwork in order etc, but I didn't wanna be a dick about it so I agreed. I returned her full deposit in 2 weeks and had a new tenant in 4 weeks after she left. I didn't charge her rent for any days after she left, and of course covered the council tax and bills in the time between her moving out and new tenant moving in. When I was cleaning up in the flat one day an officer from TV licensing called round - she hadn't paid her TV license in the 3 months of being there. I explained she no longer lived here and they said they'd just write it off.
That was some months ago. I got a call from her this morning asking for my new address. When I asked why she said she was giving it to the council to send me a council tax bill. I said I had paid the council tax between her leaving and new tenant moving in, and she said "no it's for the first 3 weeks of my tenancy when I wasn't occupying the flat" 
. I said sorry but it's up to her to pay that. She got really upset and said she can't afford it (it's £90) as she's just had to pay for the rest of the tenancy upfront - she hadn't paid any of the 3 months council tax while she was there, and paid it all yesterday minus the first 3 weeks. She said if I didn't pay she wouldn't be able to pay a vets fee for her sick dog and he'll die. They're threatening her with the magistrates court. I said sorry no, and actually because I allowed her only 5 days notice she has already saved on a nearly month's council tax bill (which I covered) which I didn't have to agree to. I didn't mention the tv license issue. She thinks I should pay it as she wasn't physically living there in that time.
I rang the council to check what they know, and they said she is disputing living in the flat for the first 3 weeks, and if that's true that I'm responsible for the bill. I've emailed over a copy of the tenancy agreement she signed as proof and waiting to hear back.
Thing is, I am on maternity leave with no 2 so not exactly rolling in it. £90 is a lot and I could do really without paying it. Legally it's her bill to pay but I feel quite bad that I've said no, especially when her dog is unwell (if she's telling the truth). AIBU to stick to my guns and refuse to pay the £90?