Several issues here that make your question unanswerable:
- Intelligence is not defined. How would you define it?
- What kind of relationship are you exactly looking for? Comparing average intelligence between groups or trying to fit a regression with intelligence on the Y-axis and relatedness to human on the X-axis?
- The general issue hidden behind methods of species comparison is "How do you define a species?"
If you want to compare average intelligence between groups, meaning that you want to compare average intelligence of a group of closely related species of human to the average intelligence of all animals? Then the answer to your question will probably be "Yes" as primates seem in average to be more intelligent than the average animal and mammals tend to be in average more intelligent than the average animal. I'd expect too that vertebrates are probably on average more intelligent than the average animal. Let's not forget that some animals have no brain (e.g. Sponge).
But now if you want to fit a regression between intelligence and relatedness to human for all animals, you will probably have some trend (a regression with a significant slope (positive correlation)), but you will have many group of points that will not fit on your line. Many birds for example may be considered as much more intelligent than humans depending on your definition. Many invertebrates such as octopuses are very intelligent, too. If you allow for a broad definition of intelligence, then you may also consider the intelligence of social insects which may be surprising. Some aquatic mammals are very intelligent although other, more seemingly stupid mammals, are closer to humans than aquatic mammals.
In short, keep in mind that intelligence is not easy to define, and depending on the definition, the answer will be different. Typically, if you use a very human-like definition of intelligence, you will probably find that intelligent species are more closely related to human. There is a correlation between intelligence and phylogeny (=tree of life), therefore yes, closely related species to humans may have some tendency to be fairly intelligent, but there are many other clades (groups of species on a phylogeny) that show some impressive intelligence, especially in insects, in mollusca, in birds, the carnivora and the cetacea.