A weapon was fired through the window of a house in Dorian Drive, Clarkston, at about 00:05 on Friday 24 June.
A 49-year-old man and his two daughters, aged 20 and 25, were uninjured in the attack.
Police spoke to people in the area on Thursday night and Friday morning. They described the response as "useful".
Det Sgt Dougie Stevenson appealed for information from anyone who saw anything suspicious in the area around the time of the incident.
"Officers went back to the scene late last night and early this morning and spoke to a number people to try and find out more information about the shooting.
"Whilst the response from the public was useful we still need people to come forward with information.
"I would ask locals or those who are usually in the area to think back to just before and after midnight between last Thursday and Friday - the night of the EU referendum - and if they recall witnessing anything suspicious in the area to contact the police."
The detective added: "This could include anyone or any car seen in suspicious circumstances, one that wasn't common to the area, or any car driving off erratically or at speed immediately following this incident.
"Local CCTV is being examined and I would like to reassure the local community that extra police patrols will remain in the area in the meantime."
Police have revisited the scene of a shooting incident in East Renfrewshire one week on in a bid to generate new leads for the inquiry.