I would stick a note through their door - see if you get any response in the next couple of days. Keep an eye on the cat and yes, perhaps phone the local vet for advice - the cat may be known to them.
Years ago, a much loved cat of mine was slowly dying. I kept taking her to the vets, asking if it was time, only for them to say she was happy, and in no pain, albeit frail and painfully thin.
One day she went missing - I spent hours combing the neighbourhood and someone eventually told me that some new people moving in a couple of doors down had taken a cat to the vet.
I spoke to them - they thought my poor girl (Siamese) was a stray and ill, so when they found her investigating their removal van, they cornered her (he got scratched and moaned at me - I wouldn't apologise because they were stupid unfeeling, insensitive f*ckers - and they took her to the RSPCA centre. RSPCA wouldn't take her in as she was sick, so they took her to a vet on the way back to pick up more stuff whilst moving - 20 miles away. I was livid when I found out - why on earth couldn't they have knocked on a few doors - everyone local knew my cat and knew the situation.
I phoned the vets, picked her up after a grilling about her condition, she was delighted to get home, but the shock had made her worse and we had to have her pts on the Monday morning. To this day, I seethe when I think of those interfering, unthinking do-gooders who hastened her death
Sorry for the rant - not sure why, as this was years ago - but a tale of why you shouldn't take action without checking, even when you think a cat is sick or neglected