I too had a cat with the same problem. She would litter in plants as well as her litter box. The vet dianosed her having a urinary track infection and prescribed special food for her, which pretty much handled the problem. Ask your vet if he carries it. I forgot the name since it was 6 yrs ago. The food is kind of expensive and if you have any more cats they will have to eat it as well. GOOD LUCK
If Tweety is a male cat then Urinary blockage is a concern and is a life threatening emergency.Urinary stones and infection are the other possibilities and although not emergencies should be addressed today as they are uncomfortable.