Absence of axial anomaly in the background of the Bohm-Aharonov vector potential

The problem of axial anomaly in the singular background of the Bohm-Aharonov gauge vector field is exactly solved. It is shown that, contrary to the leak of vacuum quantum numbers, the leak of anomaly from the singularity points does not occur. It is shown too that, in a singular background, the conventional relation between the axial anomaly and the background field strength is valid only in the space with punctures singularities