"We understand this was a distressing situation while it unfolded but we want
assure members of the public there was no imminent threat to their safety."
And the Ministry of Education has lifted the lockdown on schools and early childhood centres in the town.
Police are due to release more details about the event which has been unfolding in the last few hours.
Residents in the town were been contacted by police by text message telling them to ring 111 if they see anything suspicious.
The message from police - sent to residents via a local community emergency services network - was sent at 11.04am.
Another message has been sent in the last few minutes saying police are now "standing down".
The hunt for the armed person is thought to be connected to a high-speed chase through Rolleston earlier this morning.
Police confirmed at 11.28am that they were alerted to a report of a man in a stolen vehicle in Washdyke at just before 7am this morning.
"The man has fled from police when signalled to stop and continued to drive north towards Rakaia where he has stolen another vehicle and driven through to Rolleston where he has crashed that vehicle and fled on foot," said a spokeswoman.
"Police are in the Rolleston area making enquiries to locate the man.
"Members of the public are advised to keep their vehicles locked at this time and if they see anything that may assist us in locating this individual to contact Police on 111."
"An update will be provided when able."
A resident confirmed schools in the area were now in lockdown.
"Just to let you know that we have actioned a lockdown at (a local school) as a precaution as police have advised that they are searching for an armed offender in the Rolleston area," said a message from their child's school that they shared with the Herald.
"We are all safe and will let you know when lockdown is up - please do not come to school."
All early childhood education centres in the area have also gone into lockdown.
The Herald has contacted police for comment.