How to reduce fontsize for References when using biblatex-chicago

Since biblatex does not use thebibliography, you don't need to redefine that environment and any redefinition will not not affect the biblatex-generated bibliography.

The size of the hanging indent is controlled by the length bibhang, which is defined as

 setlength{bibhang}{ifnumequal{parindent}{0}{1em}{parindent}}

in biblatex.def and redefined to

 setlength{bibhang}{2em}

in biblatex-chicago.sty.

You could try setlength{bibhang}{parindent} or setlength{bibhang}{1em}.

documentclass{book}

usepackage[authordate,backend=biber]{biblatex-chicago}%

setlength{bibhang}{1em}

addbibresource{biblatex-examples.bib}

begin{document}
Test for reference entry autocite{sigfridsson}

printbibliography
end{document}

The font size can be changed with

renewcommand*{bibfont}{normalfontnormalsize}

Just replace normalsize with the size command for the size you want.

---

Some more details.

The default bibliography environment in biblatex-chicago is defined as

defbibenvironment{bibliography}% New for 0.9a
  {list
     {}
     {setlength{leftmargin}{bibhang}%
      setlength{itemindent}{-leftmargin}%
      setlength{itemsep}{bibitemsep}%
      setlength{parsep}{bibparsep}}}
  {endlist}
  {item}

If you want to add additional space to the left, you could say something like

documentclass{book}

usepackage[authordate,backend=biber]{biblatex-chicago}%

setlength{bibhang}{1cm}
newlength{bibleftadd}
setlength{bibleftadd}{1cm}

defbibenvironment{bibliography}
  {list
     {}
     {setlength{leftmargin}{bibhang}%
      setlength{itemindent}{-leftmargin}%
      addtolength{leftmargin}{bibleftadd}%
      setlength{itemsep}{bibitemsep}%
      setlength{parsep}{bibparsep}}}
  {endlist}
  {item}

addbibresource{biblatex-examples.bib}

begin{document}
Test for reference entry autocite{sigfridsson}

printbibliography
end{document}