What you are proposing is called "honesty testing". Many companies, especially banks, do it routinely, but are very secretive about it for obvious reasons. There are written honesty tests you can buy. Honesty tests are impossible to fool unless the person actually knows the design of the test or has specialized experience in the psychological testing field. With a written test, however, it will be obvious you are testing for honesty to any intelligent person.
You can also use plain human judgement to detect honesty levels. A dishonest person will take shortcuts in everything they do and vice versa. A dishonest person will exaggerate their accomplishments and hide negative facts. Analyze the resume to determine the extent to which it is faked up. A dishonest person will often be very calculating and disengenuous. One approach is to try to find some embarassing weakness in their background and probe them about it. If they become uncomfortable or evasive or phony, it is an indication of dishonesty. Another approach is to put them under pressure and if they begin to smile, try to make jokes or otherwise disarm you, it is an indication of a dishonest mind.
Often honesty can be determined just from appearance. A dishonest person is more likely to wear jewelry, makeup, have elaborate hairdoes and use disguise elements, like sunglasses and scarves.
A simple test for honesty is to arrange for the candidate to be in a place where they are not observed and leave a piece of trash on the floor with a trash can some distance away. If the candidate puts the trash in the trash can, they are honest. This test can be modulated. Smaller pieces of trash farther away from the can are a stronger test. You can even eliminate the can entirely. Somebody who picks up a small piece of trash and puts it in their pocket to throw it away later will be scrupulously honest, a very high bar.
A similar test is to leave a picture akilter or something knocked over. If the person corrects the problem when left alone, it is an indication of honesty.
The reason tests like these work is because an honest person is taught to think of others and be considerate, but a dishonest person will think only of themselves and act in a selfish way.