Not because Beard said she had, but because of the convincing nature of the attendant circumstances.

It was obvious that between the woman's death and the murder of Herbert Whitmore was an intimate connection, a chain whose links were undoubtedly forged by those involved in the Whitmore crime.
Beard's conduct proclaimed him antagonistic to the police investigation of his employer's death.

To place him behind bars would mean the end of his immediate activities.

Apparently he was bent on destroying evidence.
Nor was it beyond the range of probability that he was the assassin and was busy erecting safeguards for himself.
Yet Britz was reluctant to order his arrest, for he believed implicitly in the theory of giving a guilty man sufficient rope wherewith to hang himself.

The activities of a man in jail are necessarily circumscribed.
Moreover, his vigilance is never relaxed.