As CountZero has suggested, the error can be exactly duplicated in the presence of the likely typo:

>perl -wMstrict -le
"$_ = qq{chr16\t28797601\t-\t0.777877};
 my %site_info;
 ;;
 my @arr = split(/\t/,$_,4);
 $arr[0] = substr($arr[0], 3);
 $site_info{$arr[0]}{$arr[1]}{'strand'} = $arr[2];
 $site_info{$arr[0]{$arr[1]}}{'value'}  = $arr[3];
"
Can't use string ("16") as a HASH ref while "strict refs" in use at ..
+.
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And goes away and is replaced by something reasonable with the 'fixed' code:

>perl -wMstrict -le
"use Data::Dump qw(dd);
 ;;
 $_ = qq{chr16\t28797601\t-\t0.777877};
 my %site_info;
 ;;
 my @arr = split(/\t/,$_,4);
 $arr[0] = substr($arr[0], 3);
 $site_info{$arr[0]}{$arr[1]}{'strand'} = $arr[2];
 $site_info{$arr[0]}{$arr[1]}{'value'}  = $arr[3];
 ;;
 dd \%site_info;
"
{ 16 => { 28797601 => { strand => "-", value => 0.777877 } } }
[download]

Sometimes it's useful to introduce a temoprary 'convenience' variable in place of complex nested expressions:

>perl -wMstrict -le
"use Data::Dump qw(dd);
 ;;
 $_ = qq{chr16\t28797601\t-\t0.777877};
 my %site_info;
 ;;
 my @arr = split(/\t/,$_,4);
 $arr[0] = substr($arr[0], 3);
 ;;
 my $current = $site_info{$arr[0]}{$arr[1]} = {};
 $current->{'strand'} = $arr[2];
 $current->{'value'}  = $arr[3];
 ;;
 dd \%site_info;
"
{ 16 => { 28797601 => { strand => "-", value => 0.777877 } } }
[download]

Or to use slicing to do multiple, 'simultaneous' assignment:

>perl -wMstrict -le
"use Data::Dump qw(dd);
 ;;
 $_ = qq{chr16\t28797601\t-\t0.777877};
 my %site_info;
 ;;
 my @arr = split(/\t/,$_,4);
 $arr[0] = substr($arr[0], 3);
 ;;
 @{ $site_info{$arr[0]}{$arr[1]} }{ qw(strand value) } = @arr[2, 3];
 ;;
 dd \%site_info;
"
{ 16 => { 28797601 => { strand => "-", value => 0.777877 } } }
[download]