"We've got computer/phone problems. Genuine 999 calls only. Engineers working to rectify problems. Thanks for support," police said.
Police spokeswoman, Becky Tipper, told the BBC that staff came in on their off day and other neighboring police forces helped field calls, as the bank holiday caused phone lines to be "extra busy."
After about three hours a police spokesman said that systems were back up and running.
"We're pleased to confirm that all systems are now back up and running and normal bank holiday service has been resumed," he said. "We would once again like to thank everyone for their patience and support, whilst we worked to rectify matters and apologise for the inconvenience caused."
The spokesman added that police were unable to confirm if the owl survived the crash, but wished it well.
"We don't know for sure," he said. "But we certainly hope our feathered friend escaped without injury and was unaware of the feathers he ruffled, to keep us on our toes today."