How to assign null value to class object of type datetime

If your database field definition allows nulls for the Death date, then when you read it back, it will come back as System.DBNull
Check for this when you read the databse row, and assign null to your DateTime variable.

objperson._deathdate = null;

If it doesn't, then for living people assign a default death date, which could be:
1) Far in the past
2) Same as the Birth date
3) Far in the future
You can then check for this and assign a null instead.

By preference, allow a null in the database field definition for all fields which are optional, such as the death date.

I just realised that it may not be the database side that is giving you problems.

Have you declared your DateTime as a nullable type? If not, then you can never assign a true null to it.
If not, then declare it as:

DateTime? _deathdate;

and the assignment of null will work.

[edit]Added nullable type info - OriginalGriff[/edit]