Also worth noting that many, many, many people rent without rental histories. Have proof of income and you're golden.What are ways to get approved with no rental history? List Reputable References. Yes, you can rent an apartment with no rental history. But you're going to have to provide the paperwork that proves you can afford it. No, denial of a housing application cannot be based on an applicant's criminal history prior to completing the two-step process and individualized assessment. Common apartment maintenance complaints include: Unsanitary conditions, such as mold, sewage, or pests, including mice, rats, bed bugs, or roaches. If you live in Cook County, you generally cannot be denied housing just because of your arrest or conviction record. If you have untraditional rental history such as living with family explain this on your application.