There seems to be a bit of confusion on this, but apparently the answer is no with the qualifier that states can make the resettlement process very difficult.
The most thorough look at the issue seem to be this item from Think Progress:
- No, State Governors Can’t Refuse To Accept Syrian Refugees.
It refers to supreme court cases and federal laws I'll make the subject of separate posts, but the basic point seems to be that immigration policy is a nation - not a state - policy and governors cannot interfere with it. Governors are responding by claiming this is a public safety issue, which they do have jurisdiction over. And of course there's the political dimension I'll leave to the side for now.
Here's more on the specific subject.
- U.S. governors don’t have power to refuse refugees access to their states.
- States cannot refuse refugees, but they can make it difficult.
