  We consider the one dimensional Schr\"odinger operator with properly
connecting generalized point interaction at the origin. We derive a trace
formula for trace of difference of resolvents of perturbed and unperturbed
Schr\"odinger operators in terms of a Wronskian which results into an explicit
expression for perturbation determinant. Using the estimate for large time real
argument on the trace norm of the resolvent difference of the perturbed and
unperturbed Schr\"odinger operators we express the spectral shift function in
terms of perturbation determinant. Under certain integrability condition on the
potential function, we calculate low energy asymptotics for the perturbation
determinant and prove an analog of Levinson's formula.
