  In the paper arXiv:2002.12065, the authors developed a new method to compute
the exact overlap formulas between integrable boundary states and on-shell
Bethe states in integrable spin chains. This method utilizes the coordinate
Bethe ansatz representation of wave functions and singularity property of the
off-shell overlaps. In this paper, we use this new method to derive the formula
for overlaps between the Lieb-Liniger Bethe states and the Bose-Einstein
condensate (BEC) state. As a simple application this method, we obtained the
overlaps between the Lieb-Liniger eigenstates and the free particle states with
pair structure.
