This scenario pertains to Texas.
As an hourly manager, I am entitled to overtime. However, at the end of the month, on a Sunday I perform the inventory duty. This is a 10-hour shift that starts at 4 pm and ends at 2 am. I start the shift with 32 hours for the week and expect to add the 10 hours Sunday shift to have 42 hours with 2 hours of overtime. This is not the case. My manager states that the last 2 hours are part of the next week's schedule and not eligible for overtime.
While this may not sound ethical, it may be legal since the pay period ends at 11:59 on Sunday. I am looking for specific sources in FLSA or any other government case, ruling, or document that states an agreement or repudiation of this scenario.
Please keep in mind I am asking for sources for a citation. Going to HR is also an option on my list along with other forms of seeking advice. I want to keep this at the lowest level, if at all possible.

Those 2 hours are into the next weeks pay period if the pay week starts at 00:01 am Sunday and ends 12:00 Saturday at midnight. There doesn't HAVE to be a ruling..if that's when the pay week runs...thats when the pay week runs. Its been that way in the Civilian world and the Several government contracts I've been part of for 35 years.

Smoothy is correct. Overtime hours are counted during the work week. If the workweek ends during a shift the hours go towards the next week. So how many hours did you work the following week?

What is your pay period?

It appears that you hit 40 hours at midnight, the end of the pay period. At midnight the new pay period begins and you are not entitled to overtime.

Quote:

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I am looking for specific sources in FLSA or any other government case, ruling, or document that states an agreement or repudiation of this scenario.

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There are none. Consult with a local labor attorney.

You want a source; here is one: https://www.dol.gov/general/topic/wages/overtimepay

Employees covered by the Fair Labor Standards Act (FLSA) must receive overtime pay for hours worked in excess of 40 in a workweek. Notice I emphasized workweek. If your workweek ends at Midnight on Sunday then only hours worked prior to then are part of the workweek.