Disclaimers: I don't work for, or otherwise get money from, Cozy. I am not a lawyer and this is not legal advice.
I used Cozy to do the background checks on my first rental, and I'm currently using it to collect rent on that rental. So far I've been happy with the results.
Before I even advertised the house, I created an account for me at Cozy (free) and created an entry for that house (free). I also tied it to my bank account so I could collect rent (free).
I didn't use Cozy's online application. I did go in and play with building an application on their site - it has some standard questions already on it (name, address, previous addresses, etc), plus you can select from some "canned" questions to add to it, but at the time I tried it (summer 2017), I don't think it let you put in your own free-form questions. I opted to type up my own application in my favorite word processor, and I asked prospective tenants to fill it out on paper. I did not charge an application fee.
Once I had some applications in hand, I did the initial screening myself - comparing the rent to their stated income, calling their previous landlords, etc. This filtered out a few prospects.
Once I had a couple of applications I was ready to go further with, I logged in to Cozy, selected the house, and then selected the "ask for a credit/background check" option. That asks me for the prospective tenant(s) email address(es), and then sends the tenants an email with a link in it. They click on that link and it takes them to a page at Cozy where they can enter their details and pay the $40 fee. Once the checks run, I got a notification, and I could see the results at Cozy.
I ended up declining the first prospective tenant based on information in those reports. When you do that, you have to send them an "adverse action letter", which basically says that you turned them down based on something in their credit report, who you got the credit report from, and offer to give them a copy of that credit report. Cozy doesn't generate this letter for you - you have to do it yourself. I did ask Cozy support a question about something I needed to put in that letter and they responded promptly.
After I declined the first prospective tenant, I repeated the process for the second prospective tenant: go to Cozy again, selected the "ask for credit/background checks", and put in the email address of the second prospective tenant. They got an email from Cozy with a link, clicked on it, put in their details and paid the fee, and I got the reports when they were ready. I ended up accepting that tenant.
The next step is setting up the payments. Basically, I selected the entry for the house I was renting on Cozy and filled in the start date, rent due date, rent amount, and lease term. It didn't ask me for a copy of the signed lease. I then told it that John Doe, who just had a background check done, was my tenant for that house. I collected the first month's rent from the tenant in person, and made a manual entry on Cozy to show that it had been paid. If your tenant(s) are going to pay with a bank account, they need to set that up with Cozy, and I think I got a notification that the tenant had successfully set up their bank account. After that, Cozy sends the tenant an email before the rent is due each month, saying either "you need to make a payment" (if the tenant wants to authorize the payment each month) or "remember, Cozy will deduct your rent from your account on (date)" (if the tenant set up automatic payments).
I get an email when the tenant has authorized the payment, and then I get another email when the money actually hits my bank account. I don't pay anything on a per-payment basis. The tenant doesn't pay anything either, if they have the rent taken out of a bank account. If they pay by credit card, Cozy charges them 2.75% on top of the rent amount.
Cozy sits on the payments for about 5 or 6 days - that's how long it is between the "tenant paid" and "it's in my account" emails. I think, but don't know, that they're doing some kind of short-term investing with the money, which is how they pay for their service. Cozy offers an option for $3 extra (to me) per unit per month that reduces this wait time to 3 days, but I don't use it.
Some hints and kinks. 1) One of my applicants was a husband and wife, and I wanted to do the check on both of them. They only gave me one email address on their paper application, but Cozy didn't know how to send two requests to the same email address. You need to either 1) ask for two separate email addresses, and create a request in Cozy for each one, or 2) create two requests in Cozy with the same email address, but two different names. (Example: "John Doe", thedoes -at- example.com, and "Jane Doe", thedoes -at- example.com.) Only the first request will go through, so the email they get will say something like "John, please click here to run the checks." John should click on that link and fill in his information. You can then look at your Cozy dashboard for pending requests, see the link it successfully mailed John, and the link it should have mailed to Jane but didn't. You can then manually send an email (or a text or whatever) to Jane with that link, so she can click on it and fill in her information.
2) Once you've sent a prospective tenant a request to do a credit and/or background check, there isn't any way for you to cancel that request yourself. If you contact Cozy support, they can do it for you. In other words, if you have more than one prospect, only send the request to the first one, and wait for some kind of disposition on that (you accept them, you decline them, they tell you they rented elsewhere or are no longer interested) before sending the request to the second one.
3) The results of their background checks and credit checks stay online for a while at Cozy, but not forever. If I remember right, they are available for something like 15 to 30 days. If you want to keep a copy of those reports, and if it's legal for you to do so, remember to download them before they are removed from Cozy.
4) Don't be afraid to email their support if you need help. They responded promptly to my requests.
Disclaimers: I don't work for, or otherwise get money from, Cozy. I am not a lawyer and this is not legal advice.