Ashes (a potash source) from (clean) wood is good.
Ashes from coal, I am not familiar with - it may contain some chemicals (e.g., sulfur?).
Ashes form ciggs is a no, no.
While attending a Master Gardener class lecture about vegetative propagation,
and to my surprise, the lecturer advised smokers to wash their hands with soap
before starting to avoid spreading some 'tobacco virus'
(probably it is similar to FMD?).