You need to use the past participle of "overdose", in this case, which is "overdosed". This is because the sentence is a passive voice.
Example: active voice → passive voice
Our troops defeated the enemy → The enemy was defeated by our troops
The man must have eaten five hamburgers → Five hamburgers must have eaten by the man
Marilyn mailed the letter → The letter was mailed by Marilyn
Typically most sentences are active voice, i.e. We won the prize.
We — subject
won — verb
the prize — object
while a passive voice would be reversed,
The prize — object (now is subject)
was won — verb
by us — subject (now is object)
As for your question, it is actually a passive sentence. It is the same as the above except missing an object (which is fine). However, in English, passive sentence requires the verb to be a past participle.