The bare statement "I suggest you read the rules." requires a period.
Starting the sentence with may, as in "May I suggest you read the rules?"
seems to turn it into a question.
This site shows examples of may in this sense used in expressions with and without question marks:
thefreedictionary modal auxiliary verbs - may
Making a polite offer
Like can, we can use may to offer do something for someone else, though it is generally a more polite,
formal way of doing so. For example:
“May I help you set the table?”
“May we be of assistance in any way?”
As a rhetorical device
Sometimes, we use may in this way as a rhetorical device to politely introduce or emphasize an opinion or
sentiment about something, in which case we invert may with the
subject. For instance:
“May I just say, this has been the most wonderful experience of my life.”
“May we be clear that our firm will not be involved in such a dubious plan.”
“May I be frank: this is not what I was hoping for.”
To me, your original example with a question mark suggests a rising intonation, and sounds polite, while the one ending with a period suggests a flat intonation and is less polite.