Unison, whose members include a majority of Allitt's nursing colleagues at Grantham and Kesteven District Hospital in Lincolnshire, said warning signs were overlooked or ignored.
Allitt was known to have incurred self-inflicted injuries and feigned illness while a student at the hospital. Her frequent absences should have been investigated, and her family doctor asked if she was suitable for appointment as a nurse.
If a full and alarming psychological profile of Allitt was drawn, it was either unavailable to hospital management, or lost in a stretched management structure.
By several criteria, she was unfit to begin work as a nurse. Hospital authorities made 'a serious error of judgement' when they recommended Allitt for employment.
Allitt, 25, was sentenced last year to 13 life sentences for the attacks, including four murders. She is detained at Rampton special hospital in Nottinghamshire.
The union said Allitt's employment, and her recommendation by a tutor, could be explained only by staff shortages on the children's ward where she began work in February 1991. Unison's evidence, given in private to the inquiry chaired by Sir Cecil Clothier QC, focuses blame for Allitt's 58 days of attacks on events beyond the control of medical staff on the ward.
The Clothier report, which is due to be published this month, is expected to criticise four individuals - the hospital's two consultant paediatricians, Nelson Porter and Charith Nanayakkara, the nursing manager, Moira Onions, and the ward sister, Barbara Barker.
Leaked extracts of the draft Clothier report made scapegoats of the four, according to their colleagues and advisers.
Unison's evidence, which has been seen by the Independent, claims neither Mrs Onions nor Sister Barker wanted to appoint Allitt. Adult wards also refused to give her a job, and the children's ward gave her only a short contract.
'One pressure which appears to have weighed on Sister Barker in accepting Mrs Onions's decision to appoint her is that the staff had been complaining of short-staffing and Allitt was presented as, at least, 'a pair of hands',' Unison told the inquiry.
'The total number of nurses on duty at any one time gave Allitt opportunities to damage children which she may not otherwise have had.'