Let $f:X\to Y$ be a local complete intersection morphism (of schemes or varieties) of (relative) dimension $c$ everywhere. Is it true that $f^!\cong f^*[2c]$ (as a functor between the derived categories of etale constructible sheaves?), or does one really need smoothness here? What additional assumptions (or corrections) are needed here, and what is the best reference (for local complete intersection morphisms)?

Upd. As Torsten Ekedahl states, this is wrong. Still, are their any special properties of cohomology of local complete intersection morphisms (that are common with smooth morphisms, and distinguish them from general finite type morphisms)?