How do I check if variable is an array?

I have a loop over variable names and I need to check if content of a variable is an array or not:

for varname in AA BB CC; do
  local val
  if [ "$varname" is array ]; then # how can I perform this test?
    echo do something with an array
  else
    echo do something with a "'normal'" variable
  fi
done

How do I do it?