  We formulate an explicit refinement of B\"ocherer's conjecture for Siegel
modular forms of degree 2 and squarefree level, relating weighted averages of
Fourier coefficients with special values of L-functions. To achieve this, we
compute the relevant local integrals that appear in the refined global
Gan-Gross-Prasad conjecture for Bessel periods as proposed by Yifeng Liu. We
note several consequences of our conjecture to arithmetic and analytic
properties of L-functions and Fourier coefficients of Siegel modular forms.
