Yes, you say "I don't think it is the case.", rather than "I think it is not the case.", if you think something is not the case.
That is, if 'think', 'suppose', 'believe' or 'imagine' is used to introduce a negative idea, you say 'I don't think...', 'I don't suppose...', etc. The usage is called 'transferred negation'.
You also say 'I don't think so.', 'I don't suppose so.', etc - in a negative 'short answer' structure.
The word 'hope', on the other hand, is an exception, for example, you say '