I am not a serial killer crossword puzzle

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Across
  1. 2. A psychopath
  2. 4. An act punishable by law
  3. 6. An official who investigates deaths
  4. 7. Declaring something untrue
  5. 9. Not aware of what is happening around oneself
  6. 10. A statement make to inflict pain or injury
  7. 12. Someone who kills many people
  8. 13. Preserve corpse from decaying
Down
  1. 1. Likely to cause harm or injury
  2. 2. Relating to pathology
  3. 3. relating to chemistry
  4. 4. Used by butchers for chopping meat
  5. 5. An imaginary creature which is frightening
  6. 8. Main characters first name
  7. 11. No longer alive