did some research and found this documentation on OSHA's website at this url
w ww.osha.gov/SLTC/poweredindustrialtrucks/index.html
part way down the page at this url
w ww.osha.gov/pls/oshaweb/owadisp.show_document?p_table=STANDARDS&p_id=9828#1910.178(l)

in subsection 1910.178(l)(3)
the first question asked and the response from OSHA

Question 1: Is it a requirement that we checkout each forklift with a checklist at the beginning of the workday or is it a requirement for every driver throughout the day to check out the lift each time he gets one?

Reply: 29 CFR 1910.178(q)(7) has a requirement that all powered industrial trucks (PITs) be examined before being placed in service. This examination is required daily or after each shift if the trucks are used on a round-the-clock basis. Although there is no specific OSHA requirement that a checklist be used, an employer does have the responsibility to determine that PITs are properly inspected.

i read through the hole thing and hunted around for any other information and even though they do require the inspection to be done there is no mention that any records be kept or if they are how long they should be retained.

hope this confirms your question and negates any assumptions previously made ;o)