The tablet was found floating down a Blenheim river three months ago, Radio New Zealand reported.
A Blenheim woman, who did not want to be named, told RNZ she found the device tied to a soft-drink bottle on June 2 as she was walking by a river.
The tablet was slightly water damaged but was still able to be used.
The woman said she saw an email to a John Tully from his mother, asking where he was.
There was no information about any problems he had with Work and Income, RNZ said.
The mother asked the woman to send it to her, but then it broke completely, so that did not happen.
Following last week's incident, the woman realised the tablet might have belonged to the alleged shooter, so handed it over to police on Monday.
Meanwhile, the police dive squad is continuing to search the Ashburton River today.
Divers are looking for "any unrecovered personal items" that might be related to the investigation including an additional firearm and ammunition that may have been in the man's possession.
The public has been asked to stay away from the river area while the search is ongoing.
"The investigation team are continually assessing information provided by the public and media in relation to this incident," a police statement says.
"This includes reports of a tablet being handed in to Blenheim police earlier this week.
"If you believe you have any information that may help with locating the white 1985 Mitsubishi Mirage GLX or any personal items call Ashburton police on (03) 307 8411."
Information can also be provided anonymously to Crimestoppers on 0800 555 111.
Tully, 48, was charged with two counts of murdering Work and Income workers Peg Noble and Leigh Cleveland and one of attempting to murder their colleague Lindy Curtis who was seriously injured in the incident.
Tully has been remanded in custody to appear in the High Court at Christchurch on September 23.
