Animal behaviour experts at Lincoln University said owners who were neurotic were less likely to allow their cats outside.
As a result their pets had a higher chance of being overweight and 'anxious or fearful' and show behavioural problems such as scratching the furniture.
The study, published in the journal PLOS ONE, involved personality tests on 3,300 cat owners and also found that pedigree cats were more likely to be overweight.
The research builds on studies that show how parenting style can affect a child's personality. Other cat experts backed the findings.
Danielle Gunn-Moore, professor of feline medicine at Edinburgh University, said: "Cats are a mini-me. They are sentient creatures strongly affected by people around them."