The two cases happened in the early hours Cambridge Road and Burnaby Road.
Police Chief Investigation Over School
Hampshire's chief constable is under investigation by his own police and crime commissioner (PCC) over an investigation of a school hit by an alleged sex abuse scandal.
Top policeman Andy Marsh is reported to be part of an inquiry from a separate force for breach of confidentiality and contempt of court claims after his PCC Simon Hayes ordered it.
It is thought to be the first such move since by a PCC since the posts were implemented last November.
Hampshire Police are investigating rape and sex-abuse allegations involving at least two pupils at Stanbridge Earls School in Romsey.
The residential school, which caters for children with special needs aged from 10 to 19, will be closed in December after a series of damning reports over its handling of the abuse claims.
A spokesman for Hampshire's PCC office said:
"We are able to confirm that the commissioner has received a formal complaint in connection with the Stanbridge Earls School investigation.
"The allegations made are now being investigated by another police force on behalf of the commissioner and it would be entirely inappropriate to comment further at this time.''
A Hampshire police spokesman said:
"We are aware of the complaint, which is being handled by the office of the police and crime commissioner.''
The areas under investigation relate to allegations of contempt of court and breach of confidentiality in connection with the inquiry at the school, the Southern Daily Echo reported
But a PCC spokesman refused to reveal further details of the complaints or say which police force was carrying out the investigation - only that it was a Home Counties force.
Last month, education watchdog Ofsted apologised to children and parents for failing to deal properly with reports of alleged sexual abuse at the £39,000-a-year boarding school.
An inquiry by the organisation into its inspections found that three visits from 2011 to 2012 were ''problematic'' and ''each failed to get underneath concerns at the school''.
As a result, ''the judgments were not safe''. Staff were dismissed and disciplined by the watchdog as a result.
The Special Educational Needs and Disability Tribunal heavily criticised the 2011 actions of Stanbridge Earls relating to one female pupil - prompting the police probe called Operation Flamborough, which is also looking at the force's role in the investigation.
The Crown Prosecution Service did not press charges at the time as it said there was "insufficient evidence'' to provide a realistic prospect of conviction for rape.
Another pupil has since come forward alleging she suffered sexual abuse in 2010.
The vulnerable disabled youngster was said to have been raped twice in 2011 at the hands of another student and the tribunal branded the school ''unsystematic and unprofessional'' in dealing with the incident. Headteacher Peter Trythall stepped down in April.
Hampshire police have previously said their investigation into Stanbridge Earls was complex and comprehensive and they are also looking at the police handling of the allegations at the time and any new allegations.
A charity is due to take over the site and run a new school from next year after Stanbridge Earls closes.
Mr Marsh was appointed to chief constable only in January - taking over as chief constable from Alex Marshall, who left to become head of the new national college of policing.
Previously he was a deputy chief constable in Hampshire and he has also worked at Avon and Somerset Police and Wiltshire Police.
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